Haut PDF M-theory Superstrata and the MSW String

M-theory Superstrata and the MSW String

M-theory Superstrata and the MSW String

The microstate geometry corresponding to the maximally-spinning Ramond ground state of the MSW CFT is obtained by blowing up the single-center D4-D4-D4 configuration to a two-center fluxed D6-D6 configuration, whose M-theory uplift is [global AdS 3 ] × S 2 × T 6 . The addition of D0 charge via back-reacted singular D0’s was studied in [ 20 , 45 ]. The degeneracy of such “D0-halo” solutions was counted in [ 22 , 23 ], and found to give rise to an entropy that matches that of an M-theory supergraviton gas in [global AdS 3 ] × S 2 × T 6 for sufficiently small D0 charge. The full back-reaction of the supergraviton gas states has never been computed, but since our M-theory superstratum solutions represent smooth waves in AdS 3 × S 2 , one may expect that at least some of them can be thought of as coming from back-reacted supergraviton gas states. Furthermore, if the full non-Abelian and nonperturbative interactions of uplifted D0-branes results in solutions that are non-singular and varying along the M-theory circle, one expects these solutions to also resemble our M-theory superstrata. Hence, it may be that the smooth back-reacted solutions we construct are the missing link needed to connect the entropy counts in the (non-back-reacted) supergraviton gas and (singular) D0-halo approaches.
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M-theory Superstrata and the MSW String

M-theory Superstrata and the MSW String

superstrata remains to be carried out. One can also add momentum by adding M2-branes that wrap the two-sphere of the AdS 3 ×S 2 , and that carry angular momentum on both the AdS 3 and the S 2 [ 20 ]. The entropy of these configurations comes from the high degeneracy of the Landau levels that result from the dynamics of the M2-branes on the compactification manifold in the presence of M5 flux [ 61 , 20 , 62 ], and has been argued to scale in the same way as that of the black hole. The back-reaction of these “W- brane” configurations is fully worked out only in some very simple examples [ 27 ]. However, on general grounds one expects uncancelled tadpoles which give rise to asymptotics that are different from the asymptotics of bulk duals of MSW CFT states. If, on the other hand, one cancels the tadpoles using additional brane sources, there are no preserved supersymmetries whatsoever [ 28 ]. Furthermore, in more generic multi-center solutions, the corresponding W-brane configurations also give rise to tadpoles, which can only cancel when the W-branes form a closed path among the centers. 21 Hence, when the multi-center solution has a throat of finite length, these additional
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Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string

Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string

of Yang–Mills theory and the NLSM model, ref. [36] offered the first double-copy real- ization of self-dual Born–Infeld [37] scattering amplitudes. The idea that there can exist a duality between electric and magnetic field densities is as old as gauge theory. Sat- isfied by sourceless Maxwell electrodynamics, this natural duality has inspired analysis and generalizations that have been key to understanding aspects of supersymmetry, sym- metry breaking, and string theory, starting with perhaps most famously the Born–Infeld non-linear generalization of electromagnetics [38]. The emergence of duality invariance in the form of Born–Infeld scattering due to a double-copy interplay between YM and the low-energy limit of abelian Z-theory is remarkable. In concordance with the structure of open-string amplitudes given as a double copy between Yang–Mills constituents and Z- theory disk-integrals [2], the double-copy representation of Born–Infeld amplitudes as its
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Composite Anomaly in Supergravity and String Amplitude Comparison

Composite Anomaly in Supergravity and String Amplitude Comparison

nevertheless gather valuable information from such quantum gravity interactions by properly dealing with the singularities. It is in fact not just an aesthetic question to find a quantum description of grav- ity or to find a unified framework describing all four fundamental interactions but it happens to be, for modern physics, an immediate necessity because both Stan- dard Model and the concordance model of cosmology have their own deficiencies. To mention a few for the Standard Model, this theory requires almost 20 parame- ters whose values are needed to be fixed by experimental input. Some of these pa- rameters are needed to be fine-tuned upto very non-practical degrees of accuracy, which is the so-called hierarchy problem of Standard Model. In addition, the Stan- dard Model does not give satisfactory answers to neutrino mass spectrum and the strong CP problem. An ingenious way to answer the hierarchy problem is to appeal to the supersymmetry, which puts both bosonic and fermionic degrees of freedoms in terms of an underlying symmetry of the quantum theory. This set-up provides bosons and fermions of same quantum characters thereby adding elements to solve for the hierarchy problem. Moreover, the localization of supersymmetry gives rise to a supersymmetric theory of quantum gravity, called supergravity which is however again crippled with non-renormalizability issues, but its degree is milder to that of naive quantum gravity. In the observable world, supersymmetry is not manifest and thus this symmetry should be broken at the phenomenological energy scale. Thus instead of discouraging, it cues to look forward for the physics at the energy scales higher than that of common interactions which might reveal these interesting sym- metry structures.
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Higher-derivative couplings in string theory: five-point contact terms

Higher-derivative couplings in string theory: five-point contact terms

In fact, SL(2, Z) invariance of the type IIB string gives rise to some tension between the different four-point results collected in Table 1. For IIB strings, the only difference between the quartic NSNS contributions at tree level and one loop is the dilaton factor e −2φ . Other than that, the kinematic structures are identical. This means that the only way of completing the purely NSNS expressions to SL(2, Z) invariant ones is by making each term invariant and multiplying the entire expression quartic in fields by the SL(2, Z) function E 3/2(τ, ¯ τ ). In particular this means that the local U (1) symmetry of type IIB supergravity is respected by the four-particle interactions. This is indeed consistent with the results of [33,34] showing that the U (1)-violating contributions start at the level of five-particle interactions. From the other side, the four-point result including RR fields given in [18] cannot be completed to an SL(2, Z) invariant expression without modular forms that transform under weights ±1, and are hence U(1)-violating. We shall return to this issue in subsection 4.2.
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Measuring bow force in bowed string performance: Theory and implementation of a bow force sensor

Measuring bow force in bowed string performance: Theory and implementation of a bow force sensor

The interest for measuring control parameters in playing is encouraged by the advancements in the study of musical instruments by physical modeling. One advantage of this approach is that the control parameters of the model become the same as for the real instrument. On the other hand, measuring the control parameters in normal playing without interfering with normal playing conditions presents a challenge, in particular for wind instruments. The bowed stringed instruments are seemingly straight-forward to approach as the string and bow are of reasonable size and the motions associated with bowing are accessible for measurement. Application of motion capture techniques is an obvious approach for measuring bow velocity and bow-bridge distance in playing, while bow force measurements will require application of sensors to the bow or the violin. The first reliable measurement of control parameters in violin playing during real performance were made by Askenfelt [1], [2]. A bow was modified to measure bow position, bow velocity, bow-bridge distance and bow force. Bow position refers to the position of the contact point between bow hair and string relative to the frog or tip. The bow position was measured by a resistance wire running among the hairs in the outer layer of the bundle of bow hair contacting the string. The string divided the wire in two parts which were used in a branch of a Wheatstone bridge. Bow-bridge distance was measured in a similar manner, using the parts of the string on each side of the bow (wire) in a second Wheatstone bridge. Bow velocity was obtained from the bow position signal through differentiation. Bow force was measured by gluing the bow hair to two metal strips at the frog and at the tip, respectively, and measuring the deflection of the strips by strain gauges.
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Minimizing resources of sweeping and streaming string transducers

Minimizing resources of sweeping and streaming string transducers

Regular word functions extend the robust family of regular languages, preserving many of its characterizations and algorithmic properties. A word function maps words over a finite input alphabet to words over a finite output alphabet. Regular word functions have been studied in the early seventies, in the form of (deterministic) two-way finite state automata with output [1]. Engelfriet and Hoogeboom [8] later showed that monadic second-order definable graph transductions, restricted to words, are an equivalent model — this justifies the notation “regular” word functions, in the spirit of classical results in automata theory and logic by Büchi, Elgot, Rabin and others. Recently, Alur and Cerný [2] proposed an enhanced version of one-way transducers called streaming transducers, and showed that they equivalent to the two previous models. A streaming transducer processes the input word from left to right, and stores (partial) output words in finitely many, write-only registers. A variant of streaming transducers extended by stacks has been introduced in [3] and shown to capture precisely the monadic-second order definable tree transductions.
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Habemus Superstratum! A constructive proof of the existence of superstrata

Habemus Superstratum! A constructive proof of the existence of superstrata

ture that replaces the horizon of a black hole: we have directly constructed this structure in supergravity. As we emphasized in [46], this approach could have failed at many different stages throughout its development. The most recent hurdle has been to show that supergravity has structures that might contain enough states to count the entropy of the black hole. In [5] we have argued that this can happen if string theory contains three-charge superstrata solutions that can be parameterized by arbitrary continuous functions of two variables. The present paper shows explicitly that these solutions exist and furthermore that they are smooth in the duality frame where the black hole has D1,D5 and momentum charges. (It was the successful clearing of this latest hurdle that led to our somewhat celebratory title for this paper.) Though most of the recent literature on the information paradox has focused on “Alice-and-Bob” Gedankenexperiments, we believe that general quantum information arguments about physics at a black-hole horizon will always fall short of resolving the paradox: failure is inevitable without a mechanism to support structure at the horizon scale. It is remarkable that string theory can provide a natural and beautiful solution to this essential issue and, as was shown in [47], microstate geometries provide the only possible gravitational mechanism and so must be an essential part of the solution to the paradox.
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Black-Hole Microstates in String Theory : Black is the Color but Smooth are the Geometries?

Black-Hole Microstates in String Theory : Black is the Color but Smooth are the Geometries?

5.2 Systematic construction of a large family of smooth four-center solutions In this section, we present a systematic construction of the largest known family of scaling four- center smooth horizonless solutions that have the same charges as large black holes. Our construction allows us to easily build scaling four-center BPS solutions with any aspect ratios between the centers. Moreover, we focus on solutions which are asymptotically R 1,4 but the method can be adapted to any asymptotics. The main idea is to start with BPS solutions with three collinear supertube centers in Taub-NUT. As we will see, defining a parameter space where those solutions satisfy the Denef equations, the no-CTC condition and the scaling condition is rather easy. Then, the next step is to regularize the solutions at the supertube centers. As detailed in Section 4.1.3.3, this can be done by performing two or three generalized spectral flows (4.1.30). Each generalized spectral flow transforms a singular magnetic charge of its corresponding species of Supertube to a smooth KKm charge and then transforms a species of Supertube to a smooth GH center. Thus, with two spectral flows we obtain a solution with three GH centers and a Supertube. This solution is smooth in the D1-D5-P frame as explained in Section 4.1.3.3. With three spectral flows, we have a solution of four smooth GH centers in five-dimensions. Because generalized spectral flows also change the asymptotics, the last step consists in applying gauge transformations and change of background moduli to have asymptotically flat solutions.
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Towards a Higher-Dimensional String Theory for the Modeling of Computerized Systems

Towards a Higher-Dimensional String Theory for the Modeling of Computerized Systems

Music theory has been developed empirically down the ages until it achieved status as a recognized discipline. It now provides us with the means for describing the underlying mechanisms and subtle interaction between musicians as they perform, based on complex combinatory rules relating to rhythm, harmony and melody. Computer science also aims to describe the subtle organization and treatment of data. It therefore follows that the study of modeling in the field of music might lead to the discovery of concepts, abstract tools and modeling principles which are applicable to modern computer engineering.
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Anomaly constraints and string/F-theory geometry in 6D quantum gravity

Anomaly constraints and string/F-theory geometry in 6D quantum gravity

Classification of elliptically fibered Calabi-Yau manifolds It has been shown by Gross [30] that the number of distinct topological types of elliptically fibered Calabi-Yau threefolds is finite up to birational equivalence. Finiteness of the set of topologically distinct elliptically-fibered Calabi-Yau threefolds is shown in [6] using minimal surface theory and the fact that the Weierstrass form for an elliptic fibration over a fixed base has a finite number of possible distinct singularity structures. These arguments, however, do not give a clear picture of how such compactifications can be sys- tematically classified. A complete mathematical classification of elliptically fibered Calabi-Yau threefolds would be helpful in understanding the range of F-theory compactifications. The analogue of this question for four dimen- sions, while probably much more difficult, would be of even greater interest, since at this time we have very little handle on the scope of the space of four dimensional supergravity theories which can be realized through F-theory compactifications on Calabi-Yau fourfolds.
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Building blocks of closed and open string amplitudes

Building blocks of closed and open string amplitudes

The type I superstring theory is an orientifold of the closed string type IIB theory obtained by quotienting by the action of the world-sheet parity reversal Ω : (σ, τ ) → (2π − σ, τ ) (see [ 23 ] for a general review of orientifolds). At each order in perturbation, the type I superstring amplitude involves a sum of two-dimensional super-surfaces obtained from the action of the involution I(z), induced by the orientifold action Ω. The type I superstring theory contains open and closed strings, possibly non- oriented, which lead to anomaly cancellation [ 24 , 25 ] and Ramond-Ramond tadpole cancellation [ 23 , 26 ]. Closed (oriented) string amplitudes, which appear in the four closed superstring theories, are com- puted by integrals over the moduli space of super-Riemann surfaces of genus h, the number of handles, with n punctures and no boundaries. Each order in perturbation theory is weighted by the string coupling constant g s ≪ 1 to the power of the Euler characteristic of the surface, in this case g 2h−2 s .
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Sympathetic string modes in the concert harp

Sympathetic string modes in the concert harp

These experimental results can be compared to those obtained from the theory. Experi- mentally, we found two modes which mostly involve string 31 at 123.59 Hz and at 123.78 Hz. With the vibratory model, the string mode associated to string 31 is found at 123.48 Hz. Note that the model takes only one string polarization into account. The agreement between model and measurement is, as expected, very good since the tension value of each string of the simplified harp has been fixed in such a way that the eigenfrequencies of uncoupled strings correspond to those of the real instrument.
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Non-compact string backgrounds and non-rational CFT

Non-compact string backgrounds and non-rational CFT

X N S5 −→ X N S5 def = R (1|5) × (SL 2 (R) N /U(1) N × SU(2) N /U(1) N ) /Z N , with k = N + 2. Hence, the interest in NS5-branes provides strong motivation to inves- tigate string theory on the cigar. Let us also note that there exists a rich and interesting class of compactifications of NS5-branes on Calabi-Yau spaces that, by the same line of reasoning, involve the cigar as a central building block [76] (see also [7]). We should finally note that these backgrounds certainly involve some amount of supersymmetry which we suppress in our discussion here. As in the case of the analogous compact coset theories, adding supersymmetry has relatively minor effects on the world-sheet theory. Since we are more interested in the qualitative features of our non-compact coset model, we shall neglect the corrections that supersymmetry brings about, even though they are certainly important in concrete applications. For treatments of the supersymmetric models, we can refer the reader to a number of interesting recent publications [77]- [87].
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Inflation in string cosmology

Inflation in string cosmology

1.3 Observations and consequences Today, we have a few quasi-certainties about cosmology thanks to observa- tions. First the existence of dark matter was suggested by Zwicky who measured the velocity dispersions of the galaxies in the Coma cluster and found that some of the gravitational mass was missing [4]. Another solid evidence of “unseen” mass is the flatness of the rotation curves of observed galaxies that can’t be ex- plained by the visible mass of the galaxies alone [5]. The general idea is that the rotation velocity is a function of the inner mass (virial theorem). The missing matter is to be found in the dark matter halo of the galaxy. Another additional proof of the existence of dark matter is strong lensing, the light coming from distant galaxies is deviated by the presence of dark matter. Numerical simula- tions [6] highlight the necessity to include dark matter, otherwise the formation of large-scale structures does not start at the right time. Nevertheless, dark mat- ter has not been detected yet and some alternatives to DM theories have been developed. The famous MOND (MOdified Newtonian Gravity) theory tends to explain the rotation curves by a modification of Newtonian gravity for very small accelerations. This was first proposed by Milgrom [7]. But the observations of the bullet cluster [8] (see figure 1.1) are in contradiction with such theories and are strong evidence in favor of dark matter.
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The Beads-on-String Structure of Viscoelastic Threads

The Beads-on-String Structure of Viscoelastic Threads

model and show that for highly extensible molecules (as characterised by large values of the FENE extensibility parameter b > 10 3 ) there is a long intermediate elastic regime (which may extend for times of 10 20 ) in which neither the initial response of the solvent nor the nite length of the molecules is important and the chains indeed extend e ectively as in nitely extensible dumbbells with a single characteristic relaxation time. This has also been veri ed experimentally using a homologous series of polystyrene test uids with solutes of increasing molecular weight (Anna & McKinley (2001)). In the present study, we therefore do not consider the nal stages of breakup where the nite length of the polymers begins to a ect the necking process. This nal asymptotic regime has been considered for the FENE model by Entov & Hinch (1997), and more recently for the Giesekus model by Fontelos & Li (2004). In each case the extensional viscosity of the uid is bounded and the lament radius ultimately decreases linearly in time. The initial onset of this regime can also be observed in the very last stages of the experimental measurements when the thread radius has reduced to O(1 10 m); however we do not include this data in our comparison between theory and experimental observation.
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Conformal invariance and degrees of freedom in the QCD string

Conformal invariance and degrees of freedom in the QCD string

charge c of the corresponding worldsheet theory are related by α ′ M 0 2 = h − c/24 (2) where α ′ ≡ (2πσ) −1 is the Regge slope, and h is the conformal dimension of that primary field in the worldsheet theory which produces the ground state. In most cases this primary field is merely the identity field with h = 0, so that the coefficient of the pseudo-Coulomb term directly yields the corresponding central charge. In all other cases, however, the coefficient of this term yields information concerning only the difference h − c/24 ≡ −˜c/24. This is dramatically illustrated in the Ramond string: here h = c/24 = (D − 2)/16, whereupon ˜c = 0, the ground state is massless, and the long-range pseudo-Coulomb term is absent.
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The joy of string diagrams

The joy of string diagrams

the setting of monoidal categories, Hopf algebras, quantum groups, etc... , see e.g. [2]) not only for the 2-categorical machinery of adjunctions and monads, but also for recasting other basic material of category theory [3]. In this extended abstract, we content ourselves with pointing out the underlying coercions that we have to make explicit in order to treat this material graphically (see [1] for more joy!).

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D-branes and string field theory

D-branes and string field theory

The Fock module of a single string of momentum p is obtained by the action of the matter, ghost and antighost oscillators on the (ghost number one) highest weight vec[r]

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Non-perturbative Effects in String Theory

Non-perturbative Effects in String Theory

gauge group, Type I SO(32) and Type II (A and B) theories. The Heterotic theories are theories with closed strings whereas Type I and Type II contain both closed and open strings. Let us mention here a few important features of string theory which make it a good candidate for a theory of all interactions. Closed strings have a spin 2 mass- less mode which can be identified with the graviton, moreover the string perturbation theory is UV-finite thus making string theory a consistent theory of quantum gravity. Standard model-like interactions can arise from string theory. Ideas like grand unifica- tion and supersymmetry can (naturally) be incorporated in string theory. Indeed, the low energy effective field theory arising from strings is a supergravity theory. Another important feature of string theories is that they are well-defined only in ten space-time dimensions, hence they predict six extra dimensions. In order for string theory to make sense as a fundamental (or effective) theory of Nature the extra dimensions have to be small (usually compact). There are indeed solutions which allow for a spacetime of the form
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