From Heun to Painlev\'e on Sasaki-Einstein Spaces and Their Confluent Limits

The aim of this paper is to study the effect of isomonodromic deformations of the evolution of scalar fields in Sasaki-Einstein spaces in the context of holography. Here we analyze the monodromy data of the general Heun equation, resulting from a scalar on Y$^{p,q}$, thus obtaining the corresponding Painlev\'e VI equation. Furthermore we have considered limits leading to a coalescence of singularities, which in turn transform the original Painlev\'e VI equation, to one of lower rank. The confluent limits we have considered are Y$^{p,p}$, T$^{1,1} / \mathbb{Z}_2$ and Y$^{\infty, q}$.Comment: 32 pages, three figure

Semiclassical Analysis of String/Gauge Duality on Non-commutative Space

We use semiclassical method to study closed strings in the modified AdS_5*S^5 background with constant B-fields. The point-like closed strings and the streched closed strings rotating around the big circle of S^5 are considered. Quantization of these closed string leads to a time-dependent string spectrum, which we argue to correspond to the RG-flow of the dual noncommutative Yang Mills theory.Comment: 19 pages, 1 figure, revtex4. minor corrections. references adde

Circular strings in Kerr-AdS5AdS_5 black holes

The quest for extension of holographic correspondence to the case of finite temperature naturally includes Kerr-AdS black holes and their field theory duals. We probe the five-dimensional Kerr-AdS space time by pulsating strings. First we find particular pulsating string solutions and then semi-classically quantize the theory. For the string with large values of energy, we use the Bohr-Sommerfeld analysis to find the energy of the string as a function of a large quantum number. We obtain the wave function of the problem and thoroughly study the corrections to the energy, which according to the holographic dictionary are related to anomalous dimensions of certain operators in the dual gauge theory. The interpretation of results from holographic point of view is not straightforward since the dual theory is at finite temperature. Nevertheless, near or at conformal point the expressions can be thought of as the dispersion relations of stationary states.Comment: 32 pp, 1 figure; v2: Sec.3 improved, Sec.4 recalculated for a general case, typos corrected, Appendix B included; v3: Sec.3 corrected, new figure of an effective potential added, typos correcte

Gauge/String Duality

1 Dipartimento di Scienze Fisiche, Universita degli Studi di Napoli Federico II, INFN, Sezione di Napoli, Via Cintia, 80126 Napoli, Italy 2 Department of Physics, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, UK 3 Michigan Center for Theoretical Physics, The University of Michigan, Ann Arbor, MI 48109-1120, USA 4 Departamento de Fisica de Particulas, Instituto Galego de Fisica de Altas Energias (IGFAE), Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain 5 Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, 1040 Vienna, Austria 6 Department of Physics, Sofia University, 1504 Sofia, Bulgaria 7 Department of Physics, and IRMACS, Simon Fraser University, Burnaby, British Columbia, Canad

Bootstrap in Supersymmetric Liouville Field Theory. I. NS Sector

A four point function of basic Neveu-Schwarz exponential fields is constructed in the N = 1 supersymmetric Liouville field theory. Although the basic NS structure constants were known previously, we present a new derivation, based on a singular vector decoupling in the NS sector. This allows to stay completely inside the NS sector of the space of states, without referencing to the Ramond fields. The four-point construction involves also the NS blocks, for which we suggest a new recursion representation, the so-called elliptic one. The bootstrap conditions for this four point correlation function are verified numerically for different values of the parameters

Higher Equations of Motion in N = 1 SUSY Liouville Field Theory

Similarly to the ordinary bosonic Liouville field theory, in its N=1 supersymmetric version an infinite set of operator valued relations, the ``higher equations of motions'', holds. Equations are in one to one correspondence with the singular representations of the super Virasoro algebra and enumerated by a couple of natural numbers $(m,n)$. We demonstrate explicitly these equations in the classical case, where the equations of type $(1,n)$ survive and can be interpreted directly as relations for classical fields. General form of the higher equations of motion is established in the quantum case, both for the Neveu-Schwarz and Ramond series.Comment: Two references adde

Correlation functions in the Coulomb branch of N=4 SYM from AdS/CFT correspondence

In the present paper we study SU(N)->S(U(N/2)xU(N/2)) symmetry breaking in N=4 SYM via AdS/CFT correspondence. We consider two stacks of N/2 parallel D3 branes separated by a distance 2\vec d. In this case there is mixing between the different l-wave dilatonic KK modes. We calculate certain the two point correlation functions in the dual gauge theory. Due to mode mixing, the diagonal correlation functions have 1/N conformal-like correction as well as deformation terms. The off-diagonal correlators are also non-vanishing and their leading order is 1/N. We discuss briefly the spectrum of the glueball exitations.Comment: 25 pages, more comments on two throat geometry, decoupling limit and correction terms, a few typos corrected, two references added; to appear in Phys.Rev.

Semiclassical Strings, Dipole Deformations of N=1 SYM and Decoupling of KK Modes

In this paper we investigate the recently found $\gamma$-deformed Maldacena-Nunez background by studying the behavior of different semiclassical string configurations. This background is conjectured to be dual to dipole deformations of $\N=1$ SYM. We compare our results to those in the pure Maldacena-Nunez background and show that the energies of our string configurations are higher than in the undeformed background. Thinking in the lines of (hep-th/0505100) we argue that this is an evidence for better decoupling of the Kaluza-Klein modes from the pure SYM theory excitations. Moreover we are able to find a limit of the background in which the string energy is independent of $\gamma$, these strings are interpreted as corresponding to pure gauge theory effects.Comment: 31 pages, references added, new solutions in Section 7 presented, an appendix added, to appear in JHE

Instantons on ALE spaces and Super Liouville Conformal Field Theories

We provide evidence that the conformal blocks of N=1 super Liouville conformal field theory are described in terms of the SU(2) Nekrasov partition function on the ALE space O_{P^1}(-2).Comment: 10 page