On the Phase Transition of Conformal Field Theories with Holographic Duals

We study the thermodynamic relations of conformal field theories (CFTs), which are holographically dual to anti-de Sitter-Schwarzschild bulk space-times. A Cardy-Verlinde formula is derived thermodynamically for CFTs living on S^n x R with S^n having an arbitrary radius. The Hawking-Page phase transition of the CFT is described using Landau's theory of phase transitions, and an alternative derivation of the Cardy-Verlinde formula is presented. The condensate in the high temperature phase is identified as being composed of radiational matter.Comment: 10 pages, final version to appear on PL

A Regularization Scheme for the AdS/CFT Correspondence

The prescription of the AdS/CFT correspondence is refined by using a regularization procedure, which makes is possible to calculate the divergent local terms in the CFT two-point function. We present the procedure for the example of the scalar field.Comment: 5 pages, uses amsmath, amssymb packages, v2: 2 references adde

AdS_3/CFT_2 correspondence at finite temperature

The AdS/CFT correspondence is established for the AdS_3 space compactified on a solid torus with the CFT field on the boundary. Correlation functions that correspond to the bulk theory at finite temperature are obtained in the regularization a'la Gubser, Klebanov, and Polyakov. The BTZ black hole solutions in AdS_3 are T-dual to the solution in the AdS_3 space without singularity.Comment: 9pp., LaTe

Running Scaling Dimensions in Holographic Renormalization Group Flows

Holographic renormalization group flows can be interpreted in terms of effective field theory. Based on such an interpretation, a formula for the running scaling dimensions of gauge-invariant operators along such flows is proposed. The formula is checked for some simple examples from the AdS/CFT correspondence, but can be applied also in non-AdS/non-CFT cases.Comment: 14 pages, 2 figure

Boundary Terms, Spinors and Kerr/CFT

Similarly as in AdS/CFT, the requirement that the action for spinors be stationary for solutions to the Dirac equation with fixed boundary conditions determines the form of the boundary term that needs to be added to the standard Dirac action in Kerr/CFT. We determine this boundary term and make use of it to calculate the two-point function for spinor fields in Kerr/CFT. This two-point function agrees with the correlator of a two dimensional relativistic conformal field theory.Comment: 15 page

Multitrace deformations, Gamow states, and Stability of AdS/CFT

We analyze the effect of multitrace deformations in conformal field theories at leading order in a large N approximation. These theories admit a description in terms of a weakly coupled gravity dual. We show how the deformations can be mapped into boundary terms of the gravity theory and how to reproduce the RG equations found in field theory. In the case of doubletrace deformations, and for bulk scalars with masses in the range $-d^2/4<m^2<-d^2/4+1$, the deformed theory flows between two fixed points of the renormalization group, manifesting a resonant behavior at the scale characterizing the transition between the two CFT's. On the gravity side the resonance is mapped into an IR non-normalizable mode (Gamow state) whose overlap with the UV region increases as the dual operator approaches the free field limit. We argue that this resonant behavior is a generic property of large N theories in the conformal window, and associate it to a remnant of the Nambu-Goldstone mode of dilatation invariance. We emphasize the role of nonminimal couplings to gravity and establish a stability theorem for scalar/gravity systems with AdS boundary conditions in the presence of arbitrary boundary potentials and nonminimal coupling.Comment: 14 pages, references added, introduction change

Rigidly Supersymmetric Gauge Theories on Curved Superspace

In this note we construct rigidly supersymmetric gauged sigma models and gauge theories on certain Einstein four-manifolds, and discuss constraints on these theories. In work elsewhere, it was recently shown that on some nontrivial Einstein four-manifolds such as AdS$_4$, N=1 rigidly supersymmetric sigma models are constrained to have target spaces with exact K\"ahler forms. Similarly, in gauged sigma models and gauge theories, we find that supersymmetry imposes constraints on Fayet-Iliopoulos parameters, which have the effect of enforcing that K\"ahler forms on quotient spaces be exact. We also discuss general aspects of universality classes of gauged sigma models, as encoded by stacks, and also discuss affine bundle structures implicit in these constructions.Comment: 23 pages; references added; more discussion added; v4: typos fixe

Correlators of Vertex Operators for Circular Strings with Winding Numbers in AdS5xS5

We compute semiclassically the two-point correlator of the marginal vertex operators describing the rigid circular spinning string state with one large spin and one windining number in AdS_5 and three large spins and three winding numbers in S^5. The marginality condition and the conformal invariant expression for the two-point correlator obtained by using an appropriate vertex operator are shown to be associated with the diagonal and off-diagonal Virasoro constraints respectively. We evaluate semiclassically the three-point correlator of two heavy circular string vertex operators and one zero-momentum dilaton vertex operator and discuss its relation with the derivative of the dimension of the heavy circular string state with respect to the string tension.Comment: 16 pages, LaTeX, no figure