Steven S. Gubser

Large N field theories, string theory and gravity

We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N=4 supersymmetric gauge theory in four dimensions, but we discuss also field theories in other dimensions, conformal and non-conformal, with or without supersymmetry, and in particular the relation to QCD. We also discuss some implications for black hole physics.

Phases of R-charged black holes, spinning branes and strongly coupled gauge theories

We study the thermodynamic stability of charged black holes in gauged supergravity theories in D = 5, D = 4 and D = 7. We find explicitly the location of the Hawking-Page phase transition between charged black holes and the pure anti-de Sitter space-time, both in the grand-canonical ensemble, where electric potentials are held fixed, and in the canonical ensemble, where total charges are held fixed. We also find the explicit local thermodynamic stability constraints for black holes with one non-zero charge. In the grand-canonical ensemble, there is in general a region of phase space where neither the anti-de Sitter space-time is dynamically preferred, nor are the charged black holes thermodynamically stable. But in the canonical ensemble, anti-de Sitter space-time is always dynamically preferred in the domain where black holes are unstable. We demonstrate the equivalence of large R-charged black holes in D = 5, D = 4 and D = 7 with spinning near-extreme D3-, M2- and M5-branes, respectively. The mass, the charges and the entropy of such black holes can be mapped into the energy above extremality, the angular momenta and the entropy of the corresponding branes. We also note a peculiar numerological sense in which the grand-canonical stability constraints for large charge black holes in D = 4 and D = 7 are dual, and in which the D = 5 constraints are self-dual.

Continuous distributions of D3-branes and gauged supergravity

States on the Coulomb branch ofN = 4 super-Yang-Mills theory are studied from the point of view of gauged supergravity in ve dimensions. These supersymmetric solutions provide examples of consistent truncation from type-IIB supergravity in ten dimensions. A mass gap for states created by local operators and perfect screening for external quarks arise in the supergravity approximation. Weoeraninterpretationofthesesurprising featuresintermsofensembles ofbrane distributions.

Thermodynamic stability and phases of general spinning branes

We determine the thermodynamic stability conditions for near-extreme rotating D3, M5, and M2-branes with multiple angular momenta. Critical exponents near the boundary of stability are discussed and compared with a naive field theory model. From a partially numerical computation we conclude that outside the boundary of stability, the angular momentum density tends to become spatially inhomogeneous. Periodic euclidean spinning brane solutions have been studied as models of QCD. We explain how supersymmetry is restored in the world-volume field theory in a limit where spin becomes large compared to total energy. We discuss the hierarchy of energy scales that develops as this limit is approached.

Symmetric potentials of gauged supergravities in diverse dimensions and Coulomb branch of gauge theories

A class of conformally flat and asymptotically anti--de Sitter geometries involving profiles of scalar fields is studied from the point of view of gauged supergravity. The scalars involved in the solutions parametrize the SL(N,R)/SO(N) submanifold of the full scalar coset of the gauged supergravity, and are described by a symmetric potential with a universal form. These geometries descend via consistent truncation from distributions of D3-branes, M2-branes, or M5-branes in ten or eleven dimensions. We exhibit analogous solutions asymptotic to AdS{sub 6} which descend from the D4-D8-brane system. We obtain the related six-dimensional theory by consistent reduction from massive type IIA supergravity. All our geometries correspond to states in the Coulomb branch of the dual conformal field theories. We analyze linear fluctuations of minimally coupled scalars and find both discrete and continuous spectra, but always bounded below.

Generalized conifolds and four dimensional Script N = 1 superconformal theories

This paper lays groundwork for the detailed study of the non-trivial renormalization group flow connecting supersymmetric fixed points in four dimensions using string theory on AdS spaces. Specifically, we consider D3-branes placed at singularities of Calabi-Yau threefolds which generalize the conifold singularity and have an ADE classification. The

Generalized Conifolds and 4d N=1 SCFT

\mathcal{N}=1

Renormalization group flows from holography supersymmetry and a c theorem

superconformal theories dictating their low-energy dynamics are infrared fixed points arising from deforming the corresponding ADE

Modeling the fifth dimension with scalars and gravity

\mathcal{N}=2

AdS / CFT and gravity

superconformal field theories by mass terms for adjoint chiral fields. We probe the geometry with a single