Benjamin A. Burrington

Holographic duals of flavored N = 1 super Yang-Mills: beyond the probe approximation

We construct backreacted D3/D7 supergravity backgrounds which are dual to four-dimensional N = 1 and N = 2 supersymmetric Yang-Mills at large Nc with ∞avor quarks in the fundamental representation of SU(Nc). We take into account the backreaction of D7-branes on either AdS5£S 5 or AdS5£T 1;1 , or more generically on backgrounds where the space transverse to the D3-branes is Kahler. The construction of the backreacted geometry splits into two stages. First we determine the modiflcation of the six-dimensional space transverse to the D3 due to the D7, and then we compute the warp factor due to the D3. TheN = 2 background corresponds to placing a single stack of Nf D7-branes in AdS5£S 5 . Here the Kahler potential is known exactly, while the warp factor is obtained in certain limits as a perturbative expansion. By placing another D7 0 probe in the backreacted D3/D7 background, we derive the efiect of the D7-branes on the spectrum of the scalar ∞uctuations to flrst order in Nf. The two systems with N = 1 supersymmetry that we discuss are D3/D7/D7 0 and D3/D7 on the conifold. In both cases, the Kahler potential is obtained perturbatively in the number of D7-branes. We provide all the ingredients necessary for the computation of each term in the expansion, and in each case give the flrst few terms explicitly. Finally, we comment on some aspects of the dual gauge theories.

Lifshitz-like black brane thermodynamics in higher dimensions

Gravitational backgrounds in d+2 dimensions have been proposed as holographic duals to Lifshitz-like theories describing critical phenomena in d + 1 dimensions with critical exponent z 1. We numerically explore a dilatonEinstein-Maxwell model admitting such backgrounds as solutions. Such backgrounds are characterized by a temperature T and chemical potential , and we nd how to embed these solutions into AdS for a range of values of z and d. We nd no thermal instability going from the T to the T regimes, regardless of the dimension, and nd that the solutions smoothly interpolate

Towards supergravity duals of chiral symmetry breaking in Sasaki-Einstein cascading quiver theories

We construct a flrst order deformation of the complex structure of the cone over Sasaki-Einstein spaces Y p;q and check supersymmetry explicitly. This space is a central element in the holographic dual of chiral symmetry breaking for a large class of cascading quiver theories. We discuss a solution describing a stack of N D3 branes and M fractional D3 branes at the tip of the deformed spaces.

Operator mixing for string states in the D1-D5 CFT near the orbifold point

In the context of the fuzzball programme, we investigate deforming the microscopic string description of the D1-D5 system on T^4xS^1 away from the orbifold point. Using conformal perturbation theory and a generalization of Lunin-Mathur symmetric orbifold technology for computing twist-nontwist correlators developed in a companion work, we initiate a program to compute the anomalous dimensions of low-lying string states in the D1-D5 superconformal field theory. Our method entails finding four-point functions involving a string operator O of interest and the deformation operator, taking coincidence limits to identify which other operators mix with O, subtracting the identified conformal family to isolate other contributions to the four-point function, finding the mixing coefficients, and iterating. For the lowest-lying string modes, this procedure should truncate in a finite number of steps. We check our method by showing how the operator dual to the dilaton does not participate in mixing that would change its conformal dimension, as expected. Next we complete the first stage of the iteration procedure for a low-lying string state of the form \partial X \partial X \bar\partial X \bar\partial X and find its mixing coefficient. Our main qualitative result is evidence of operator mixing at first order in the deformation parameter, which means that the string state acquires an anomalous dimension. After diagonalization this will mean that anomalous dimensions of some string states in the D1-D5 SCFT must decrease away from the orbifold point while others increase.

Twist-nontwist correlators in

We consider general 2D orbifold CFTs of the form M^N/S_N, with M a target space manifold and S_N the symmetric group, and generalize the Lunin-Mathur covering space technique in two ways. First, we consider excitations of twist operators by modes of fields that are not twisted by that operator, and show how to account for these excitations when computing correlation functions in the covering space. Second, we consider non-twist sector operators and show how to include the effects of these insertions in the covering space. We work two examples, one using a simple bosonic CFT, and one using the D1-D5 CFT at the orbifold point. We show that the resulting correlators have the correct form for a 2D CFT.

M^N/S_N

The D1D5 conformal field theory has provided a useful microscopic model for studying black holes. The coupling in this theory is a twist deformation whose action on the vacuum generates a squeezed state. We give a new derivation of the expression for this squeezed state using the conformal Ward identity; this derivation provides an insight into several features of the state. We also examine the squeezed state in a continuum limit where we describe it in terms of position space correlations created by the twist.

orbifold CFTs

Abstract We show by direct construction that a large class of quiver gauge theories admits actions of finite Heisenberg groups. We consider various quiver gauge theories that arise as AdS/CFT duals of orbifolds of C 3 , the conifold and its orbifolds and some orbifolds of the cone over Y p , q . Matching the gauge theory analysis with string theory on the corresponding spaces implies that the operators counting wrapped branes do not commute in the presence of flux.

Analyzing the squeezed state generated by a twist deformation

We examine the leading Regge string states relevant for semi-classical spinning string solutions. Using elementary RNS techniques, quadratic terms in an effective Lagrangian are constructed which describe massive NSNS strings in a space-time with five-form flux. We then examine the specific case of AdS5 ×S 5 , finding the dependence of AdS “energy” (E0) on spin in AdS (S), spin on the sphere (J), and orbital angular momentum on the sphere (∇a∇ a ).

Finite Heisenberg groups in quiver gauge theories

We examine the leading Regge string states relevant for semi-classical spinning string solutions. Using elementary RNS techniques, quadratic terms in an effective Lagrangian are constructed which describe massive NSNS strings in a space-time with five-form flux. We then examine the specific case of AdS5 ×S 5 , finding the dependence of AdS “energy” (E0) on spin in AdS (S), spin on the sphere (J), and orbital angular momentum on the sphere (∇a∇ a ).

Spinning strings in AdS5×S5: A worldsheet perspective

Abstract Many conformal quiver gauge theories admit nonconformal generalizations. These generalizations change the rank of some of the gauge groups in a consistent way, inducing a running in the gauge couplings. We find a group of discrete transformations that acts on a large class of these theories. These transformations form a central extension of the Heisenberg group, generalizing the Heisenberg group of the conformal case, when all gauge groups have the same rank. In the AdS/CFT correspondence the nonconformal quiver gauge theory is dual to supergravity backgrounds with both five-form and three-form flux. A direct implication is that operators counting wrapped branes satisfy a central extension of a finite Heisenberg group and therefore do not commute.