Gaetano Bertoldi

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

Non-critical superstrings from four-dimensional gauge theory

We study large-N double-scaling limits of U(N) gauge theories in four dimensions. We focus on theories in a partially confining phase where an abelian subgroup Ĝ of the gauge group remains unconfined. Double-scaling is defined near critical points in the parameter/moduli space where states charged under Ĝ become massless. In specific cases, we present evidence that the double-scaled theory is dual to a non-critical superstring background. Models studied include the β-deformation of = 4 SUSY Yang-Mills which leads to a non-critical string theory with sixteen supercharges. We also study = 1 SUSY Yang-Mills theory coupled to a single chiral superfield with a polynomial superpotential which leads to a related string theory with eight supercharges. In both cases the string coupling is small and the background is free from Ramond-Ramond flux.

N = 2 supersymmetric Yang-Mills renormalization group scale as modulus for Witten-Dijkgraaf-Verlinde-Verlinde equations

We derive a new set of WDVV equations for N = 2 SYM in which the renormalization scale Λ is identified with the distinguished modulus which naturally arises in topological field theories.

Beta function, C-theorem and WDVV equations in 4D N=2 SYM

Abstract We show that the exact beta -function of 4D N =2 SYM plays the role of the metric whose inverse satisfies the WDVV-like equations F ikl β lm F mnj = F jkl β lm F mni . The conjecture that the WDVV-like equations are equivalent to the identity involving the u -modulus and the prepotential F , seen as a superconformal anomaly, sheds light on the recently considered c-theorem for the N =2 SYM field theories.

Double scaling limits and twisted non-critical superstrings

We consider double-scaling limits of multicut solutions of certain one matrix models that are related to Calabi-Yau singularities of type A and the respective topological B model via the Dijkgraaf-Vafa correspondence. These double-scaling limits naturally lead to a bosonic string with c ≤ 1. We argue that this non-critical string is given by the topologically twisted non-critical superstring background which provides the dual description of the double-scaled little string theory at the Calabi-Yau singularity. The algorithms developed recently to solve a generic multicut matrix model by means of the loop equations allow to show that the scaling of the higher genus terms in the matrix model free energy matches the expected behaviour in the topological B-model. This result applies to a generic matrix model singularity and the relative double-scaling limit. We use these techniques to explicitly evaluate the free energy at genus one and genus two.

Large N gauge theories and topological cigars

We analyze the conjectured duality between a class of double-scaling limits of a one-matrix model and the topological twist of non-critical superstring backgrounds that contain the N = 2 Kazama-Suzuki SL(2)/U(1) supercoset model. The untwisted backgrounds are holographically dual to double-scaled Little String Theories in four dimensions and to the large N double-scaling limit of certain supersymmetric gauge theories. The matrix model in question is the auxiliary Dijkgraaf-Vafa matrix model that encodes the F-terms of the above supersymmetric gauge theories. We evaluate matrix model loop functions with the goal of extracting information on the spectrum of operators in the dual non-critical bosonic string. The twisted coset at level one, the topological cigar, is known to be equivalent to the c = 1 non-critical string at selfdual radius and to the topological theory on a deformed conifold. In this case, we find that the matrix model double-scaling limit describes a subset of the full spectrum of the c = 1 theory at selfdual radius. In particular, it contains operators that do not satisfy the Seiberg bound.

Zamolodchikov relations and Liouville hierarchy in SL(2,R)k WZNW model

We study the connection between Zamolodchikov operator-valued relations in Liouville field theory and in the SL(2,R)k WZNW model. In particular, the classical relations in SL(2,R)k can be formulated as a classical Liouville hierarchy in terms of the isotopic coordinates, and their covariance is easily understood in the framework of the AdS3/CFT2 correspondence. Conversely, we find a closed expression for the classical Liouville decoupling operators in terms of the so-called uniformizing Schwarzian operators and show that the associated uniformizing parameter plays the same role as the isotopic coordinates in SL(2,R)k. The solutions of the jth classical decoupling equation in the WZNW model span a spin j reducible representation of SL(2,R). Likewise, we show that in Liouville theory solutions of the classical decoupling equations span spin j representations of SL(2,R), which is interpreted as the isometry group of the hyperbolic upper half-plane.

Zamolodchikov operator-valued relations for SL(2,R)_k WZNW model

An infinite set of operator-valued relations that hold for reducible representations of the sl(2)ˆk algebra is derived. These relations are analogous to those recently obtained by Zamolodchikov which involve logarithmic fields associated to the Virasoro degenerate representations in Liouville theory. The fusion rules of the sl(2)ˆk algebra turn out to be a crucial step in the analysis. The possible relevance of these relations for the boundary theory in the AdS3/CFT2 correspondence is suggested.