Jose D. Edelstein

Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity

We explore the relation between positivity of the energy constraints in conformal field theories and causality in their dual gravity description. Our discussion involves CFTs with different central charges whose description, in the gravity side, requires the inclusion of quadratic curvature corrections. It is enough, indeed, to consider the Gauss-Bonnet term. We find that both sides of the AdS/CFT correspondence impose a restriction on the Gauss-Bonnet coupling. In the case of 6d supersymmetric CFTs, we show the full matching of these restrictions. We perform this computation in two ways. First by considering a thermal setup in a black hole background. Second by scrutinizing the scattering of gravitons with a shock wave in AdS. The different helicities provide the corresponding lower and upper bounds. We generalize these results to arbitrary higher dimensions and comment on some hints and puzzles they prompt regarding the possible existence of higher dimensional CFTs and the extent to which the AdS/CFT correspondence would be valid for them.

Causality in AdS/CFT and Lovelock theory

We explore the constraints imposed on higher curvature corrections of the Lovelock type due to causality restrictions in the boundary of asymptotically AdS spacetime. In the framework of AdS/CFT, this is related to positivity of the energy constraints that arise in conformal collider physics. We present explicit analytic results that fully address these issues for cubic Lovelock gravity in arbitrary dimensions and give the formal analytic results that comprehend general Lovelock theory. The computations can be performed in two ways, both by considering a thermal setup in a black hole background and by studying the scattering of gravitons with a shock wave in AdS. We show that both computations coincide in Lovelock theory. The different helicities, as expected, provide the boundaries defining the region of allowed couplings. We generalize these results to arbitrary higher dimensions and discuss their consequences on the shear viscosity to energy density ratio of CFT plasmas, the possible existence of Boulware-Deser instabilities in Lovelock theory and the extent to which the AdS/CFT correspondence might be valid for arbitrary dimensions.

Jet quenching at finite `t Hooft coupling and chemical potential from AdS/CFT

Following the nonperturbative prescription for the jet quenching parameter recently proposed by Liu, Rajagopal and Wiedemann, we compute the first correction in the inverse `t Hooft coupling corresponding to string α corrections in the dual background. We also consider the introduction of a chemical potential for the U(1)3 gauged R-symmetry. While the former mildly diminishes the jet quenching parameter –this suggesting a smooth interpolation between the strong coupling and perturbative results–, the latter generically increases its value. We comment on the extension of this setup to quarks of finite mass.

Lovelock theories, holography and the fate of the viscosity bound

We consider Lovelock theories of gravity in the context of AdS/CFT. We show that, for these theories, causality violation on a black hole background can occur well in the interior of the geometry, thus posing more stringent constraints than were previously found in the literature. Also, we find that instabilities of the geometry can appear for certain parameter values at any point in the geometry, as well in the bulk as close to the horizon. These new sources of causality violation and instability should be related to CFT features that do not depend on the UV behavior. They solve a puzzle found previously concerning unphysical negative values for the shear viscosity that are not ruled out solely by causality restrictions. We find that, contrary to previous expectations, causality violation is not always related to positivity of energy. Furthermore, we compute the bound for the shear viscosity to entropy density ratio of supersymmetric conformal field theories from du2009=u20094 till du2009=u200910 — i.e., up to quartic Lovelock theory –, and find that it behaves smoothly as a function of d. We propose an approximate formula that nicely fits these values and has a nice asymptotic behavior when d → ∞ for any Lovelock gravity. We discuss in some detail the latter limit. We finally argue that it is possible to obtain increasingly lower values for η/s by the inclusion of more Lovelock terms.

Supersymmetric branes on AdS5 × Yp,q and their field theory duals

We systematically study supersymmetric embeddings of D-brane probes of different dimensionality in the AdS5 × Y p,q background of type IIB string theory. The main technique employed is the kappa symmetry of the probes worldvolume theory. In the case of D3-branes, we recover the known three-cycles dual to the dibaryonic operators of the gauge theory and we also find a new family of supersymmetric embeddings. The BPS fluctuations of dibaryons are analyzed and shown to match the gauge theory results. Supersymmetric configurations of D5-branes, representing domain walls, and of spacetime filling D7-branes (which can be used to add flavor) are also found. We also study the baryon vertex and some other embeddings which break supersymmetry but are nevertheless stable.

Whitham hierarchies, instanton corrections and soft supersymmetry breaking in N = 2 SU(N) super Yang-Mills theory

We study N = 2 super Yang-Mills theory with gauge group SU(N) from the point of view of the Whitham hierarchy. We develop a new recursive method to compute the whole instanton expansion of the prepotential using the theta function associated with the root lattice of the group. Explicit results for the one- and two-instanton corrections in SU(N) are presented. Interpreting the slow times of the hierarchy as additional couplings, we show how they can be promoted to spurion superfields that softly break N = 2 supersymmetry down to N = 0. This provides a family of non-supersymmetric deformations of the theory, associated with higher Casimir operators of the gauge group. The SU(3) theory is analyzed in some detail.

Resurgent Transseries and the Holomorphic Anomaly

The gauge theoretic large N expansion yields an asymptotic series which requires a nonperturbative completion to be well defined. Recently, within the context of random matrix models, it was shown how to build resurgent transseries solutions encoding the full nonperturbative information beyond the ’t Hooft genus expansion. On the other hand, via large N duality, random matrix models may be holographically described by B-model closed topological strings in local Calabi–Yau geometries. This raises the question of constructing the corresponding holographically dual resurgent transseries, tantamount to nonperturbative topological string theory. This paper addresses this point by showing how to construct resurgent transseries solutions to the holomorphic anomaly equations. These solutions are built upon (generalized) multi-instanton sectors, where the instanton actions are holomorphic. The asymptotic expansions around the multi-instanton sectors have both holomorphic and anti-holomorphic dependence, may allow for resonance, and their structure is completely fixed by the holomorphic anomaly equations in terms of specific polynomials multiplied by exponential factors and up to the holomorphic ambiguities—which generalizes the known perturbative structure to the full transseries. In particular, the anti-holomorphic dependence has a somewhat universal character. Furthermore, in the non-perturbative sectors, holomorphic ambiguities may be fixed at conifold points. This construction shows the nonperturbative integrability of the holomorphic anomaly equations and sets the ground to start addressing large-order analysis and resurgent nonperturbative completions within closed topological string theory.

Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local CP 2

The holomorphic anomaly equations describe B-model closed topological strings in Calabi–Yau geometries. Having been used to construct perturbative expansions, it was recently shown that they can also be extended past perturbation theory by making use of resurgent transseries. These yield formal nonperturbative solutions, showing integrability of the holomorphic anomaly equations at the nonperturbative level. This paper takes such constructions one step further by working out in great detail the specific example of topological strings in the mirror of the local

Lie-algebra expansions, Chern-Simons theories and the Einstein-Hilbert lagrangian

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