In the limit of infinite radius de Sitter space becomes locally flat and the static patch tends to Rindler space. A holographic description of the static patch must result in a holographic description of some flat space theory, expressed in Rindler coordinates. Given such a holographic theory how does one decode the hologram and determine the bulk flat space theory, its particle spectrum, forces, and bulk quantum fields? In this paper we will answer this question for a particular case: DSSYK at infinite temperature and show that the bulk theory is a strongly coupled version of the ’t Hooft model, i.e., (1+1)-dimensional QCD, with a single quark flavor. It may also be thought of as an open string theory with mesons lying on a single Regge trajectory.

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Shoichiro Miyashita

Japan

Yasuhiro Sekino

United States

Leonard Susskind

DSSYK at infinite temperature: the flat-space limit and the ’t Hooft model

A surprising connection exists between double-scaled SYK at infinite temperature, and large $\textit{N}$ QCD. The large $\textit{N}$ expansions of the two theories have the same form; the ’t Hooft limit of QCD parallels the fixed $\textit{p}$ limit of SYK (for a theory with $\textit{p}$-fermion interactions), and the limit of fixed gauge coupling $\textit{g}$ — the flat space limit in AdS/CFT — parallels the double-scaled limit of SYK. From the holographic perspective fixed $\textit{g}$ is the far more interesting limit of gauge theory, but very little is known about it. DSSYK allows us to explore it in a more tractable example. The connection is illustrated by perturbative and non-perturbative DSSYK calculations, and comparing the results with known properties of Yang Mills theory.

Double-scaled SYK, QCD, and the flat space limit of de Sitter space

Abstract We consider the gauge/gravity correspondence between maximally supersymmetric Yang–Mills theory in (p + 1) dimensions and superstring theory on the near-horizon limit of the Dp-brane solution. The string-frame metric is AdS$_{p + 2}$ × S$^{8 − p}$ times a Weyl factor, and there is no conformal symmetry except for p = 3. In a previous paper by one of the present authors, the free-field result of gauge theory has been reproduced from string theory for a particular operator that has angular momentum along S$^{8 − p}$. In this paper, we extend this result to operators that have angular momenta along AdS$_{p + 2}$. Our approach is based on a Euclidean formulation proposed by Dobashi et al. [Nucl. Phys. B 665, 94 (2003)] and on the “string bit” picture. We first show that the spinning string solution in Lorentzian AdS, found by Gubser et al. [Nucl. Phys. B 636, 99 (2002)], can be recast in a form that connects two points on the boundary of Euclidean AdS. The transition amplitudes of such strings can be interpreted as gauge theory correlators. We study the case of zero gauge coupling by ignoring interactions among string bits (massless particles in 10D spacetime that constitute a string), and show that the free-field results of gauge theory are reproduced.

Tomotaka Kitamura

Rotating particles in AdS: Holography at weak gauge coupling and without conformal symmetry

Abstract Gauge/gravity correspondence is regarded as a powerful tool for the study of strongly coupled quantum systems, but its proof is not available. An unresolved issue that should be closely related to the proof is what kind of correspondence exists, if any, when gauge theory is weakly coupled. We report progress about this limit for the case associated with D-branes (), namely, the duality between the D maximally supersymmetric Yang–Mills theory and superstring theory on the near-horizon limit of the D-brane solution. It has been suggested by supergravity analysis that the two-point functions of certain operators in gauge theory obey a power law with the power different from the free-field value for . In this work, we show for the first time that the free-field result can be reproduced by superstring theory on the strongly curved background. The operator that we consider is of the form , where  is a complex combination of two scalar fields. We assume that the corresponding string has the worldsheet spatial direction discretized into  bits, and use the fact that these bits become non-interacting when ’t Hooft coupling is zero.

Evidence for weak-coupling holography from the gauge/gravity correspondence for D -branes

We consider an open universe created by bubble nucleation, and study possible effects of our “ancestor vacuum,” a de Sitter space in which bubble nucleation occurred, on the present universe. We compute vacuum expectation values of the energy-momentum tensor for a minimally coupled scalar field, carefully taking into account the effect of the ancestor vacuum by the Euclidean prescription. We pay particular attention to the so-called supercurvature mode, a non-normalizable mode on a spatial slice of the open universe, which has been known to exist for sufficiently light fields. This mode decays in time most slowly, and may leave residual effects of the ancestor vacuum, potentially observable in the present universe. We point out that the vacuum energy of the quantum field can be regarded as dark energy if mass of the field is of order the present Hubble parameter or smaller. We obtain preliminary results for the dark energy equation of state <math><mi>w</mi><mo>(</mo><mi>z</mi><mo>)</mo></math> as a function of the redshift.