Agostino Butti

The baryonic branch of Klebanov-Strassler solution: a supersymmetric family of SU(3) structure backgrounds

We exhibit a one-parameter family of regular supersymmetric solutions of type IIB theory that describes the baryonic branch of the Klebanov-Strassler (KS) theory. The solution is obtained by applying the supersymmetry conditions for SU(3)-structure manifolds to an interpolating ansatz proposed by Papadopoulos and Tseytlin. Other than at the KS point, the family does not have a conformally-Ricci-flat metric, neither it has self-dual three-form flux. By varying also the string coupling, our solution smoothly interpolates between Klebanov-Strassler and Maldacena-Nu?ez (MN). The asymptotic IR and UV are that of KS throughout the interpolating flow, except for the extremal value of the parameter where the UV solution drastically changes to MN.

The Dual superconformal theory for L**pqr manifolds

We present the superconformal gauge theory living on the world-volume of D3 branes probing the toric singularities with horizon the recently discovered Sasaki-Einstein manifolds Lp,q,r. Various checks of the identification are made by comparing the central charge and the R-charges of the chiral fields with the information that can be extracted from toric geometry. Fractional branes are also introduced and the physics of the associated duality cascade discussed.

R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization

We conjecture a general formula for assigning R-charges and multiplicities for the chiral fields of all gauge theories living on branes at toric singularities. We check that the central charge and the dimensions of all the chiral fields agree with the information on volumes that can be extracted from toric geometry. We also analytically check the equivalence between the volume minimization procedure discovered in hep-th/0503183 and a-maximization, for the most general toric diagram. Our results can be considered as a very general check of the AdS/CFT correspondence, valid for all superconformal theories associated with toric singularities.

Counting BPS baryonic operators in CFTs with Sasaki-Einstein duals

We study supersymmetric D3 brane configurations wrapping internal cycles of type II backgrounds AdS5 × H for a generic Sasaki-Einstein manifold H. These configurations correspond to BPS baryonic operators in the dual quiver gauge theory. In each sector with given baryonic charge, we write explicit partition functions counting all the BPS operators according to their flavor and R-charge. We also show how to extract geometrical information about H from the partition functions; in particular, we give general formulae for computing volumes of three cycles in H.

On the geometry and the moduli space of beta-deformed quiver gauge theories

We consider a class of super-conformal β-deformed = 1 gauge theories dual to string theory on AdS5 × X with fluxes, where X is a deformed Sasaki-Einstein manifold. The supergravity backgrounds are explicit examples of Generalised Calabi-Yau manifolds: the cone over X admits an integrable generalised complex structure in terms of which the BPS sector of the gauge theory can be described. The moduli spaces of the deformed toric = 1 gauge theories are studied on a number of examples and are in agreement with the moduli spaces of D3 and D5 static and dual giant probes.

Deformations of toric singularities and fractional branes

Fractional branes added to a large stack of D3-branes at the singularity of a Calabi-Yau cone modify the quiver gauge theory breaking conformal invariance and leading to different kinds of IR behaviors. For toric singularities admitting complex deformations we propose a simple method that allows to compute the anomaly free rank distributions in the gauge theory corresponding to the fractional deformation branes. This algorithm fits Altmanns rule of decomposition of the toric diagram into a Minkowski sum of polytopes. More generally we suggest how different IR behaviors triggered by fractional branes can be classified by looking at suitable weights associated with the external legs of the (p,q) web. We check the proposal on many examples and match in some interesting cases the moduli space of the gauge theory with the deformed geometry.

Deformations of conformal theories and non-toric quiver gauge theories

We discuss several examples of non-toric quiver gauge theories dual to Sasaki-Einstein manifolds with U(1)2 or U(1) isometry. We give a general method for constructing non-toric examples by adding relevant deformations to the toric case. For all examples, we are able to make a complete comparison between the prediction for R-charges based on geometry and on quantum field theory. We also give a general discussion of the spectrum of conformal dimensions for mesonic and baryonic operators for a generic quiver theory; in the toric case we make an explicit comparison between R-charges of mesons and baryons.

On the nature of the finite-temperature transition in QCD

We investigate the nature of the finite-temperature transition in QCD with Nf massless flavors. Universality arguments show that a continuous phase transition may exist only if there is a stable fixed point in the three-dimensional ?4 theory characterized by the symmetry-breaking pattern [SU(Nf)L?SU(Nf)R]/(Nf)V?SU(Nf)V/(Nf)V, or [U(Nf)L?U(Nf)R]/U(1)V?U(Nf)V/U(1)V if the U(1)A symmetry is effectively restored at Tc. In order to determine the fixed points of these ?4 theories, we exploit a three-dimensional perturbative approach in which physical quantities are expanded in powers of renormalized quartic couplings. We compute the perturbative expansion of the ?-functions to six loops and determine their large-order behavior. No stable fixed point is found, except for Nf = 2 corresponding to the symmetry-breaking pattern SO(4)?SO(3). Therefore, the finite-temperature phase transition in QCD is of first order for Nf ? 3. A continuous phase transition is allowed only for Nf = 2. But, since the theory with symmetry-breaking pattern [U(2)L?U(2)R]/U(1)?U(2)V/U(1) does not have stable fixed points, the transition can be continuous only if the effective breaking of the U(1)A symmetry is sufficiently large.

The critical equation of state of the three-dimensional O(N) universality class: N>4

Abstract We determine the scaling equation of state of the three-dimensional O ( N ) universality class, for N = 5 , 6 , 32 , 64 . The N = 5 model is relevant for the SO ( 5 ) theory of high- T c superconductivity, while the N = 6 model is relevant for the chiral phase transition in two-color QCD with two flavors. We first obtain the critical exponents and the small-field, high-temperature, expansion of the effective potential (Helmholtz free energy) by analyzing the available perturbative series, in both fixed-dimension and e-expansion schemes. Then, we determine the critical equation of state by using a systematic approximation scheme, based on polynomial representations valid in the whole critical region, which satisfy the known analytical properties of the equation of state, take into account the Goldstone singularities at the coexistence curve and match the small-field, high-temperature, expansion of the effective potential. This allows us also to determine several universal amplitude ratios. We also compare our approximate solutions with those obtained in the large- N expansion, up to order 1 / N , finding good agreement for N ≳ 32 .