arXiv subjects

Alberto Zaffaroni

Publications and source records attributed to Alberto Zaffaroni.

At least 73 records · Page 4Linked to original sources

arXiv2008

Mastering the Master Space

Supersymmetric gauge theories have an important but perhaps under-appreciated notion of a master space, which controls the full moduli space. For world-volume theories of D-branes probing a Calabi-Yau singularity X the situation is particularly illustrative. In the case of one physical brane, the master space F is the space of F-terms and a particular quotient thereof is X itself. We study various properties of F which encode such physical quantities as Higgsing, BPS spectra, hidden global symmetries, etc. Using the plethystic program we also discuss what happens at higher number N of branes. This letter is a summary and some extensions of the key points of a longer companion paper arXiv:0801.1585.

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arXiv2007

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

We consider a class of super-conformal beta-deformed N=1 gauge theories dual to string theory on $AdS_5 \times X$ 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 N=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.

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arXiv2007

Counting BPS Baryonic Operators in CFTs with Sasaki-Einstein duals

We study supersymmetric D3 brane configurations wrapping internal cycles of type II backgrounds AdS(5) x 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.

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arXiv2007

Counting Chiral Operators in Quiver Gauge Theories

We discuss in detail the problem of counting BPS gauge invariant operators in the chiral ring of quiver gauge theories living on D-branes probing generic toric CY singularities. The computation of generating functions that include counting of baryonic operators is based on a relation between the baryonic charges in field theory and the Kaehler moduli of the CY singularities. A study of the interplay between gauge theory and geometry shows that given geometrical sectors appear more than once in the field theory, leading to a notion of "multiplicities". We explain in detail how to decompose the generating function for one D-brane into different sectors and how to compute their relevant multiplicities by introducing geometric and anomalous baryonic charges. The Plethystic Exponential remains a major tool for passing from one D-brane to arbitrary number of D-branes. Explicit formulae are given for few examples, including C^3/Z_3, F_0, and dP_1.

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arXiv2007

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.

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arXiv2007

Baryonic Generating Functions

We show how it is possible to use the plethystic program in order to compute baryonic generating functions that count BPS operators in the chiral ring of quiver gauge theories living on the world volume of D branes probing a non compact CY manifold. Special attention is given to the conifold theory and the orbifold C^2/Z_2 times C, where exact expressions for generating functions are given in detail. This paper solves a long standing problem for the combinatorics of quiver gauge theories with baryonic moduli spaces. It opens the way to a statistical analysis of quiver theories on baryonic branches. Surprisingly, the baryonic charge turns out to be the quantized Kahler modulus of the geometry.

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arXiv2006

Gravity duals to deformed SYM theories and Generalized Complex Geometry

We analyze the supersymmetry conditions for a class of SU(2) structure backgrounds of Type IIB supergravity, corresponding to a specific ansatz for the supersymmetry parameters. These backgrounds are relevant for the AdS/CFT correspondence since they are suitable to describe mass deformations or beta-deformations of four-dimensional superconformal gauge theories. Using Generalized Complex Geometry we show that these geometries are characterized by a closed nowhere-vanishing vector field and a modified fundamental form which is also closed. The vector field encodes the information about the superpotential and the type of deformation - mass or beta respectively. We also show that the Pilch-Warner solution dual to a mass-deformation of N =4 Super Yang-Mills and the Lunin-Maldacena beta-deformation of the same background fall in our class of solutions.

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arXiv2005

From Toric Geometry to Quiver Gauge Theory: the Equivalence of a-maximization and Z-minimization

AdS/CFT predicts a precise relation between the central charge a, the scaling dimensions of some operators in the CFT on D3-branes at conical singularities and the volumes of the horizon and of certain cycles in the supergravity dual. We review how a quantitative check of this relation can be performed for all toric singularities. In addition to the results presented in hep-th/0506232, we also discuss the relation with the recently discovered map between toric singularities and tilings; in particular, we discuss how to find the precise distribution of R-charges in the quiver gauge theory using dimers technology.

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arXiv2005

The dual superconformal theory for Lpqr 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 L^{p,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.

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arXiv2005

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.

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arXiv2005

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 interpolates between Klebanov-Strassler (KS) and Maldacena-Nunez (MN). 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. Nevertheless, the asymptotic IR and UV are that of KS troughout the family, except for the extremal value of the interpolating parameter where the UV solution drastically changes to MN. This one-parameter family of solutions is interpreted as the dual of the baryonic branch of gauge theory, confirming the expecation that the KS solution corresponds to a particular symmetric point in the branch.

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arXiv2000

3D superconformal theories from Sasakian seven-manifolds: new nontrivial evidences for AdS_4/CFT_3

In this paper we discuss candidate superconformal N=2 gauge theories that realize the AdS/CFT correspondence with M--theory compactified on the homogeneous Sasakian 7-manifolds M^7 that were classified long ago. In particular we focus on the two cases M^7=Q^{1,1,1} and M^7=M^{1,1,1}, for the latter the Kaluza Klein spectrum being completely known. We show how the toric description of M^7 suggests the gauge group and the supersingleton fields. The conformal dimensions of the latter can be independently calculated by comparison with the mass of baryonic operators that correspond to 5-branes wrapped on supersymmetric 5-cycles and are charged with respect to the Betti multiplets. The entire Kaluza Klein spectrum of short multiplets agrees with these dimensions. Furthermore, the metric cone over the Sasakian manifold is a conifold algebraically embedded in some C^p. The ring of chiral primary fields is defined as the coordinate ring of C^p modded by the ideal generated by the embedding equations; this ideal has a nice characterization by means of representation theory. The entire Kaluza Klein spectrum is explained in terms of these vanishing relations. We give the superfield interpretation of all short multiplets and we point out the existence of many long multiplets with rational protected dimensions, whose presence and pattern seem to be universal in all compactifications.

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arXiv1999

Monopoles in String Theory

A realization of E_{n+1} monopoles in string theory is given. The NS five brane stuck to an Orientifold eight plane is identified as the 't Hooft Polyakov monopole. Correspondingly, the moduli space of many such NS branes is identified with the moduli space of SU(2) monopoles. These monopoles transform in the spinor representation of an SO(2n) gauge group when n D8 branes are stacked upon the orientifold plane. This leads to a realization of E_{n+1} monopole moduli spaces. Charge conservation leads to a dynamical effect which does not allow the NS branes to leave the orientifold plane. This suggests that the monopole moduli space is smooth for n<8. Odd n>8 obeys a similar condition. Using a chain of dualities, we also connect our system to an Heterotic background with Kaluza-Klein monopoles.

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arXiv1999

Issues on Orientifolds: On the brane construction of gauge theories with SO(2n) global symmetry

We discuss issues related to orientifolds and the brane realization for gauge theories with orthogonal and symplectic groups. We specifically discuss the case of theories with (hidden) global SO(2n) symmetry, from three to six dimensions. We analyze mirror symmetry for three dimensional N=4 gauge theories, Brane Box Models and six-dimensional gauge theories. We also discuss the issue of T-duality for D_n space-time singularities. Stuck D branes on ON^0 planes play an interesting role.

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arXiv1998

On N=8 Supergravity on $AdS_5$ and N=4 Superconformal Yang-Mills theory

We discuss the spectrum of states of IIB supergravity on $AdS_5\times S^5$ in a manifest $SU(2,2/4)$ invariant setting. The boundary fields are described in terms of N=4 superconformal Yang-Mills theory and the proposed correspondence between supergravity in $AdS_5$ and superconformal invariant singleton theory at the boundary is formulated in an N=4 superfield covariant language.

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arXiv1998

Branes and Six Dimensional Supersymmetric Theories

We consider configurations of six-branes, five-branes and eight-branes in various superstring backgrounds. These configurations give rise to $(0,1)$ supersymmetric theories in six dimensions. The condition for RR charge conservation of a brane configuration translates to the condition that the corresponding field theory is anomaly-free. Sets of infinitely many models with non-trivial RG fixed points at strong coupling are demonstrated. Some of them reproduce and generalise the world-volume theories of SO(32) and $E_8\times E_8$ small instantons. All the models are shown to be connected by smooth transitions. In particular, the small instanton transition for which a tensor multiplet is traded for 29 hypermultiplets is explicitly demonstrated. The particular limit in which these theories can be considered as six-dimensional string theories without gravity are discussed. New fixed points (string theories) associated with $E_n$ global symmetries are discovered by taking the strong string coupling limit.

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arXiv1997

Confinement and Strings in MQCD

We study aspects of confinement in the M theory fivebrane version of QCD (MQCD). We show heavy quarks are confined in hadrons (which take the form of membrane-fivebrane bound states) for N=1 and softly broken N=2 SU(Nc) MQCD. We explore and clarify the transition from the exotic physics of the latter to the standard physics of the former. In particular, the many strings and quark-antiquark mesons found in N=2 field theory by Douglas and Shenker are reproduced. It is seen that in the N=1 limit all but one such meson disappears while all of the strings survive. The strings of softly broken N=2, N=1, and even non-supersymmetric SU(Nc) MQCD have a common ratio for their tensions as a function of the amount of flux they carry. We also comment on the almost BPS properties of the Douglas-Shenker strings and discuss the brane picture for monopole confinement on N=2 QCD Higgs branches.

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arXiv1997

Chiral Symmetry from Type IIA Branes

We propose a mechanism in which, using an eightbrane, a sixbrane ends on a NS brane in type IIA superstring theory. We use this mechanism to construct N=1 supersymmetric gauge theories in four dimensions with chiral matter localized in different points in space. Anomaly cancellation for the gauge theories is satisfied by requiring RR charge conservation for the various type IIA fields. The construction allows us to study a curious phase transition in which the number of flavors in supersymmetric QCD depends on the value of the ten dimensional cosmological constant. These phenomena are related to the fact that every time a D8-brane crosses a NS brane, a D6-brane is created in between them.

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