Dual String Theory Research Articles

D-brane charges in gravitational duals of 2 + 1 dimensional gauge theories and duality cascades

We perform a systematic analysis of the D-brane charges associated with string theory realizations of d=3 gauge theories, focusing on the examples of the N=4 supersymmetric U(N)xU(N+M) Yang-Mills theory and the N=3 supersymmetric U(N)xU(N+M) Yang-Mills-Chern-Simons theory. We use both the brane construction of these theories and their dual string theory backgrounds in the supergravity approximation. In the N=4 case we generalize the previously known gravitational duals to arbitrary values of the gauge couplings, and present a precise mapping between the gravity and field theory parameters. In the N=3 case, which (for some values of N and M) flows to an N=6 supersymmetric Chern-Simons-matter theory in the IR, we argue that the careful analysis of the charges leads to a shift in the value of the B-field in the IR solution by 1/2, in units where its periodicity is one, compared to previous claims. We also suggest that the N=3 theories may exhibit, for some values of N and M, duality cascades similar to those of the Klebanov-Strassler theory.

BPS operators from the Wilson loop in the 3-dimensional supersymmetric Chern-Simons theory

We consider the small deformation of the point-like Wilson loop in the 3-dimensional $\mathcal{N}=6$ superconformal Chern-Simons theory. By Taylor expansion of the point-like Wilson loop in powers of the loop variables, we obtain the BPS operators that correspond to the excited string states of the dual IIA string theory on the pp wave background. The BPS conditions of the Wilson loop constrain both the loop variables and the forms of the operators obtained in the Taylor expansion.

The topology of the triple Pomeron vertex in [formula omitted] SYM

We investigate, within N=4 SYM, the high energy behavior in the triple Regge limit of a six point correlator of R-currents. Using the leading logarithmic approximation, we sum all diagrams whose color lines fit onto the surface of a sphere. We find three distinct classes of graphs, and one of them contains the triple Pomeron vertex known from QCD. We present results which, within the AdS/CFT correspondence, can be compared with scattering amplitudes in the dual string theory.

Moduli Spaces of Instantons on the Taub-NUT Space

We present ADHM-Nahm data for instantons on the Taub-NUT space and encode these data in terms of Bow Diagrams. We study the moduli spaces of the instantons and present these spaces as finite hyperkähler quotients. As an example, we find an explicit expression for the metric on the moduli space of one SU(2) instanton. We motivate our construction by identifying a corresponding string theory brane configuration. By following string theory dualities we are led to supersymmetric gauge theories with impurities.

Diffractive vector meson photoproduction from dual string theory

We study diffractive vector-meson photoproduction using string theory via AdS/CFT. The large s behavior of the cross sections for the scattering of the vector meson V on a proton is dominated by the soft Pomeron, {sigma}{sub V}{approx}s{sup 2{epsilon}}{sup -2{alpha}{sub P}{sup '}}{sup /B}, where from the string theory model of [arXiv:hep-th/0501039], {epsilon} is approximately 1/7 below 10 GeV, and 1/11 for higher, but still sub-Froissart, energies. This is due to the production of black holes in the dual gravity. In {phi} photoproduction the mesonic Regge poles do not contribute, so that we deal with a pure Pomeron contribution. This allows for an experimental test. At the gauge theory 'Planck scale' of about 1-2 GeV, the ratios of the soft Pomeron contributions to the photoproduction cross sections of different vector mesons involve not only the obvious quark model factors, but also the Boltzmann factors e{sup -4M{}sub V}{sup /T{}sub 0}, with T{sub 0} the temperature of the dual black hole. The presence of these factors is confirmed in the experimental data for {rho}, {omega}, {phi}, J/{psi}, and {psi}(2S) photoproduction and is compatible with the meager {upsilon} photoproduction data. Throughout, we use vector-meson dominance, and from the data we obtain T{sub 0} of aboutmore » 1.3 GeV, i.e. the gauge theory ''Planck scale,'' as expected. The ratio of the experimental soft Pomeron onset scale E-circumflex{sub R}{approx}9 GeV and of the gauge theory Planck scale, T{sub 0}{approx}1.3 GeV, conforms to the theoretical prediction of N{sub c}{sup 2}/N{sub c}{sup 1/4}.« less

1/Neffects in non-relativistic gauge-gravity duality

We argue that higher-curvature terms in the gravitational Lagrangian lead, via non-relativistic gauge-gravity duality, to finite renormalization of the dynamical exponent of the dual conformal field theory. Our argument includes a proof of the non-renormalization of the Schrodinger and Lifshitz metrics beyond rescalings of their parameters, directly generalizing the AdS case. We use this effect to construct string-theory duals of non-relativistic critical systems with non-integer dynamical exponents, then use these duals to predict the viscosity/entropy ratios of these systems. The predicted values weakly violate the KSS bound.

The Virtual Photon Structure Functions and AdS/QCD Correspondence

We study the virtual photon structure functions from gauge/string duality. If the Bjorken variable x is not small, supergravity approximation becomes good in dual string theory. We calculate the virtual photon structure functions at large 't Hooft coupling in a moderate x-region and determine x-behavior of the structure functions. We also show that the Callan-Gross relation F_L=0 is satisfied to a good approximation in gravity calculation.

Baryon dissociation in a strongly coupled plasma

Using the dual string theory, we study a circular baryonic configuration in a wind of strongly coupled N=4 Yang-Mills plasma blowing in the plane of the baryon, before and after a quark has dissociated from it. A simple enough model that captures many interesting features is when there are four quarks in the baryon. As a step towards phenomenology, we compare representative dissociated configurations, and make some comments about their energetics and other properties. Related results that we find include the observation that the screening length formula L_s T ~ (1-v^2)^{1/4} obtained previously for other color singlet configurations, is robust for circular baryons as well.

Hot spacetimes for cold atoms

Building on our earlier work and that of Son, we construct string theory duals of non-relativistic critical phenomena at finite temperature and density. Concretely, we find black hole solutions of type IIB supergravity whose asymptotic geometries realize the Schroedinger group as isometries. We then identify the non-relativistic conformal field theories to which they are dual. We analyze the thermodynamics of these black holes, which turn out to describe the system at finite temperature and finite density. The strong-coupling result for the shear viscosity of the dual non-relativistic field theory saturates the KSS bound.

Fractional M2-branes

We consider two generalizations of the = 6 superconformal Chern-Simons-matter theories with gauge group U(N) × U(N). The first generalization is to = 6 superconformal U(M) × U(N) theories, and the second to = 5 superconformal O(2M) × USp(2N) and O(2M+1) × USp(2N) theories. These theories are conjectured to describe M2-branes probing C4/Zk in the unitary case, and C4/k in the orthogonal/symplectic case, together with a discrete flux, which can be interpreted as |M−N| fractional M2-branes localized at the orbifold singularity. The classical theories with these gauge groups have been constructed before; in this paper we focus on some quantum aspects of these theories, and on a detailed description of their M theory and type IIA string theory duals.

Wilson loops in 3-dimensional 𝒩 = 6 supersymmetric Chern-Simons theory and their string theory duals

We study Wilson loops in the three-dimensional N=6 supersymmetric Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena, that is conjectured to be dual to type IIA string theory on AdS_4 x CP^3. We construct loop operators in the Chern-Simons theory which preserve 1/6 of the supercharges and calculate their expectation value up to 2-loop order at weak coupling. The expectation value at strong coupling is found by constructing the string theory duals of these operators. For low dimensional representations these are fundamental strings, for high dimensional representations these are D2-branes and D6-branes. In support of this identification we demonstrate that these string theory solutions match the symmetries, charges and the preserved supersymmetries of their Chern-Simons theory counterparts.

Big bang/big crunch cosmologies in matrix theory and AdS/CFT

Recently several versions of gauge-gravity duality in string theory have been used to understand null and space-like singularities. In many cases, the gauge theory description allows a smooth evolution across what appears as a singularity in the gravity description.

On deformed gauge theories and their string/M-theory duals

We present general formulae for the TsT transformation (T-duality, shift, T-duality) of type II string backgrounds and open string boundary conditions. The TsT transformation provides a systematic procedure to find string theory duals of gauge theories with deformed products of fields in the lagrangian, and the duals can be analyzed by using transformed D-brane probes. As examples illustrating some features of the deformed theories, we consider the known backgrounds dual to non-commutative, dipole and β-deformed N = 4 Super Yang-Mills as well as new backgrounds dual to deformations of the recently proposed N = 6 Chern-Simons-matter theory living on multiple M2-branes on an orbifold. © 2008 SISSA.

On cancellations of ultraviolet divergences in supergravity amplitudes

AbstractConcrete calculations have pointed out that amplitudes in perturbative gravity exhibit unanticipated cancellations taming their ultraviolet behaviour independently of supersymmetry. Similar ultraviolet behaviour of 𝒩 = 4 super‐Yang‐Mills and 𝒩 = 8 maximal supergravity has explicitly been observed until three loops. The cancellations can be connected to two manifest features of gravitational theories: firstly gauge invariance from diffeomorphism symmetries and secondly that amplitudes are colourless and exhibits crossing symmetry. We will discuss these two properties in turn as well as the rôle of supersymmetry and string theory dualities in the structure of multiloop amplitudes in supergravity.

On a worldsheet dual of the Gaussian matrix model

We discuss a modification of Gopakumar's prescription for constructing string theory duals of free gauge theories. We use this prescription to construct an unconventional worldsheet dual of the Gaussian matrix model.

Supergravity description of boost invariant conformal plasma at strong coupling

We study string theory duals of the expanding boost invariant conformal gauge theory plasmas at strong coupling. The dual supergravity background is constructed as an asymptotic late-time expansion, corresponding to equilibration of the gauge theory plasma. The absence of curvature singularities in the first few orders of the late-time expansion of the dual gravitational background unambiguously determines the equilibrium equation of state, and the shear viscosity of the gauge theory plasma. While the absence of the leading pole singularities in the gravitational curvature invariants at third order in late-time expansion determines the relaxation time of the plasma, the subleading logarithmic singularity cannot be canceled within a supergravity approximation. Thus, a supergravity approximation to a dual description of the strongly coupled boost invariant expanding plasma is inconsistent. Nevertheless we find that the relaxation time determined from the cancellation of pole singularities is quite robust.

The space-time operator product expansion in string theory duals of field theories

We study the operator product expansion (OPE) limit of correlation functions in field theories which possess string theory duals, from the point of view of the string worldsheet. We show how the interesting (single-trace) terms in the OPE of the field theory arise in this limit from the OPE of the worldsheet theory of the string dual, using a dominant saddle point which appears in computations of worldsheet correlation functions in the space-time OPE limit. The worldsheet OPE generically contains only non-physical operators, but all the non-physical contributions are resummed by the saddle point to a contribution similar to that of a physical operator, which exactly matches the field theory expectations. We verify that the OPE limit of the worldsheet theory does not have any other contributions to the OPE limit of space-time correlation functions. Our discussion is completely general and applies to any local field theory (conformal at high energies) that has a weakly coupled string theory dual (with arbitrary curvature). As a first application, we compare our results to a proposal of R. Gopakumar for the string theory dual of free gauge theories.

A holographic computation of the central charges ofd= 4, 𝒩 = 2 SCFTs

We use the AdS/CFT correspondence to compute the central charges of the d = 4, = 2 superconformal field theories arising from N D3-branes at singularities in F-theory. These include the conformal theories with En global symmetries. We compute the central charges a and c related to the conformal anomaly, and also the central charges k associated to the global symmetry in these theories. All of these are related to the coefficients of Chern-Simons terms in the dual string theory on AdS5. Our computation is exact for all values of N, enabling several tests of the dualities recently proposed by Argyres and Seiberg for the E6 and E7 theories with N = 1.

Holographic renormalization of gravity in little string theory duals

We perform a holographic renormalization of gravity duals to little string theories. In particular, we construct counterterms which yield a well-defined type II action for NS-sector linear dilaton backgrounds. Our methods are based on a similar recent construction in asymptotically flat spacetimes, and our work demonstrates in detail the parallels between asymptotically flat and linear dilaton boundary conditions. The counterterms guarantee that (i) the on-shell action is finite and (ii) asymptotically linear dilaton solutions are stationary points of the action under all boundary condition preserving variations. We use the resulting action to compute a boundary stress tensor and the associated conserved charges.

On K3 surfaces with large complex structure

We discuss a notion of large complex structure for elliptic K3 surfaces with section inspired by the eight-dimensional F-theory/heterotic duality in string theory. This concept is naturally associated with the Type II Mumford partial compactification of the moduli space of periods for these structures. The paper provides an explicit Hodge-theoretic condition for the complex structure of an elliptic K3 surface with section to be large. We also establish certain geometric consequences of this large complex structure condition in terms of the Kodaira types of the singular fibers of the elliptic fibration.