Dario Martelli

Comments on string theory backgrounds with non-relativistic conformal symmetry

We consider non-relativistic conformal quantum mechanical theories that arise by doing discrete light cone quantization of field theories. If the field theory has a gravity dual, then the conformal quantum mechanical theory can have a gravity dual description in a suitable finite temperature and finite density regime. Using this we compute the thermodynamic properties of the system. We give an explicit example where we display both the conformal quantum mechanical theory as well as the gravity dual. We also discuss the string theory embedding of certain backgrounds with non-relativistic conformal symmetry that were recently discussed. Using this, we construct finite temperature and finite density solutions, with asymptotic non-relativistic conformal symmetry. In addition, we derive consistent Kaluza-Klein truncations of type IIB supergravity to a five dimensional theory with massive vector fields.

Gauge theories from toric geometry and brane tilings

We provide a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi-Yau singularity. Our method combines information from the geometry and topology of Sasaki-Einstein manifolds, AdS/CFT, dimers, and brane tilings. We explain how the field content, quantum numbers, and superpotential of a superconformal gauge theory on D3-branes probing a toric Calabi-Yau singularity can be deduced. The infinite family of toric singularities with known horizon Sasaki-Einstein manifolds La,b,c is used to illustrate these ideas. We construct the corresponding quiver gauge theories, which may be fully specified by giving a tiling of the plane by hexagons with certain gluing rules. As checks of this construction, we perform a-maximisation as well as Z-minimisation to compute the exact R-charges of an arbitrary such quiver. We also examine a number of examples in detail, including the infinite subfamily La,b,a, whose smallest member is the Suspended Pinch Point.

Superstrings with intrinsic torsion

We analyze the necessary and sufficient conditions for the preservation of supersymmetry for bosonic geometries of the form

Toric Geometry, Sasaki–Einstein Manifolds and a New Infinite Class of AdS/CFT Duals

{R}^{1,9\ensuremath{-}d}\ifmmode\times\else\texttimes\fi{}{M}_{d},

An infinite family of superconformal quiver gauge theories with Sasaki-Einstein duals.

in the common Neveu-Schwarz\char21{}Neveu-Schwarz (NS-NS) sector of type II string theory and also type I or heterotic string theory. The results are phrased in terms of the intrinsic torsion of G structures and provide a comprehensive classification of static supersymmetric backgrounds in these theories. Generalized calibrations naturally appear since the geometries can always arise as solutions describing NS or type I or heterotic fivebranes wrapping calibrated cycles. Some new solutions are presented. In particular we find

Toric Sasaki–Einstein metrics on S2×S3

d=6

Supersymmetric AdS5 solutions of type IIB supergravity

examples with a fibered structure which preserve

Moduli spaces of Chern-Simons quiver gauge theories and AdS(4)/CFT(3)

\mathcal{N}=1,2,3

Fivebranes Wrapped on SLAG Three-Cycles and Related Geometry

supersymmetry in type II and include compact type I or heterotic geometries.

Obstructions to the existence of Sasaki-Einstein metrics

Recently an infinite family of explicit Sasaki–Einstein metrics Yp,q on S2×S3 has been discovered, where p and q are two coprime positive integers, with q<p. These give rise to a corresponding family of Calabi–Yau cones, which moreover are toric. Aided by several recent results in toric geometry, we show that these are Kähler quotients namely the vacua of gauged linear sigma models with charges (p,p,−p+q,−p−q), thereby generalising the conifold, which is p=1,q=0. We present the corresponding toric diagrams and show that these may be embedded in the toric diagram for the orbifold for all q<p with fixed p. We hence find that the Yp,q manifolds are AdS/CFT dual to an infinite class of superconformal field theories arising as IR fixed points of toric quiver gauge theories with gauge group SU(N)2p. As a non–trivial example, we show that Y2,1 is an explicit irregular Sasaki–Einstein metric on the horizon of the complex cone over the first del Pezzo surface. The dual quiver gauge theory has already been constructed for this case and hence we can predict the exact central charge of this theory at its IR fixed point using the AdS/CFT correspondence. The value we obtain is a quadratic irrational number and, remarkably, agrees with a recent purely field theoretic calculation using a-maximisation.