arXiv subjects

A. Lerda

Publications and source records attributed to A. Lerda.

At least 37 records · Page 2Linked to original sources

arXiv2019

Two-point correlators in non-conformal $\mathcal{N}=2$ gauge theories

We study the two-point correlation functions of chiral/anti-chiral operators in $N=2$ supersymmetric Yang-Mills theories on $R^4$ with gauge group SU(N) and $N_f$ massless hypermultiplets in the fundamental representation. We compute them in perturbation theory, using dimensional regularization up to two loops, and show that field-theory observables built out of dimensionless ratios of two-point renormalized correlators on $R^4$ are in perfect agreement with the same quantities computed using localization on the four-sphere, even in the non-conformal case $N_f\not=2N$.

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arXiv2018

Surface operators, dual quivers and contours

We study half-BPS surface operators in four dimensional N=2 SU(N) gauge theories, and analyze their low-energy effective action on the four dimensional Coulomb branch using equivariant localization. We also study surface operators as coupled 2d/4d quiver gauge theories with an SU(N) flavour symmetry. In this description, the same surface operator can be described by different quivers that are related to each other by two dimensional Seiberg duality. We argue that these dual quivers correspond, on the localization side, to distinct integration contours that can be determined by the Fayet-Iliopoulos parameters of the two dimensional gauge nodes. We verify the proposal by mapping the solutions of the twisted chiral ring equations of the 2d/4d quivers onto individual residues of the localization integrand.

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arXiv2018

Surface operators in 5d gauge theories and duality relations

We study half-BPS surface operators in 5d N=1 gauge theories compactified on a circle. Using localization methods and the twisted chiral ring relations of coupled 3d/5d quiver gauge theories, we calculate the twisted chiral superpotential that governs the infrared properties of these surface operators. We make a detailed analysis of the localization integrand, and by comparing with the results from the twisted chiral ring equations obtain constraints on the 3d and 5d Chern-Simons levels so that the instanton partition function does not depend on the choice of integration contour. For these values of the Chern-Simons couplings, we comment on how the distinct quiver theories that realize the same surface operator are related to each other by Aharony-Seiberg dualities.

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arXiv2018

Correlators between Wilson loop and chiral operators in N=2 conformal gauge theories

We consider conformal N=2 super Yang-Mills theories with gauge group SU(N) and Nf=2N fundamental hypermultiplets in presence of a circular 1/2-BPS Wilson loop. It is natural to conjecture that the matrix model which describes the expectation value of this system also encodes the one-point functions of chiral scalar operators in presence of the Wilson loop. We obtain evidence of this conjecture by successfully comparing, at finite N and at the two-loop order, the one-point functions computed in field theory with the vacuum expectation values of the corresponding normal-ordered operators in the matrix model. For the part of these expressions with transcendentality zeta(3), we also obtain results in the large-N limit that are exact in the 't Hooft coupling lambda.

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arXiv2017

Surface operators, chiral rings, and localization in N=2 gauge theories

We study half-BPS surface operators in supersymmetric gauge theories in four and five dimensions following two different approaches. In the first approach we analyze the chiral ring equations for certain quiver theories in two and three dimensions, coupled respectively to four- and five-dimensional gauge theories. The chiral ring equations, which arise from extremizing a twisted chiral superpotential, are solved as power series in the infrared scales of the quiver theories. In the second approach we use equivariant localization and obtain the twisted chiral superpotential as a function of the Coulomb moduli of the four- and five-dimensional gauge theories, and find a perfect match with the results obtained from the chiral ring equations. In the five-dimensional case this match is achieved after solving a number of subtleties in the localization formulas which amounts to choosing a particular residue prescription in the integrals that yield the Nekrasov-like partition functions for ramified instantons. We also comment on the necessity of including Chern-Simons terms in order to match the superpotentials obtained from dual quiver descriptions of a given surface operator.

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arXiv2017

Modular and duality properties of surface operators in N=2* gauge theories

We calculate the instanton partition function of the four-dimensional N=2* SU(N) gauge theory in the presence of a generic surface operator, using equivariant localization. By analyzing the constraints that arise from S-duality, we show that the effective twisted superpotential, which governs the infrared dynamics of the two-dimensional theory on the surface operator, satisfies a modular anomaly equation. Exploiting the localization results, we solve this equation in terms of elliptic and quasi-modular forms which resum all non-perturbative corrections. We also show that our results, derived for monodromy defects in the four-dimensional theory, match the effective twisted superpotential describing the infrared properties of certain two-dimensional sigma models coupled either to pure N=2 or to N=2* gauge theories.

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arXiv2017

Two-point Correlators in N=2 Gauge Theories

We consider two-point correlators in SU(N) gauge theories on R4 with N=2 supersymmetry and Nf massless hypermultiplets in the fundamental representation. Using localization on S4, we compute the leading perturbative corrections to the two-point functions of chiral/anti-chiral operators made of scalar fields. The results are compared at two and three loops against direct field theory computations for some special operators whose correlators remain finite in perturbation theory at the specific loop order. In the conformal case, the match is shown up to two loops for a generic choice of operators and for arbitrary N.

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arXiv2016

Chiral observables and S-duality in N = 2* U(N) gauge theories

We study N = 2* theories with gauge group U(N) and use equivariant localization to calculate the quantum expectation values of the simplest chiral ring elements. These are expressed as an expansion in the mass of the adjoint hypermultiplet, with coefficients given by quasi-modular forms of the S-duality group. Under the action of this group, we construct combinations of chiral ring elements that transform as modular forms of definite weight. As an independent check, we confirm these results by comparing the spectral curves of the associated Hitchin system and the elliptic Calogero-Moser system. We also propose an exact and compact expression for the 1-instanton contribution to the expectation value of the chiral ring elements.

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arXiv2016

S-duality, triangle groups and modular anomalies in N=2 SQCD

We study N = 2 superconformal theories with gauge group SU(N) and 2N fundamental flavours in a locus of the Coulomb branch with a Z_N symmetry. In this special vacuum, we calculate the prepotential, the dual periods and the period matrix using equivariant localization. When the flavours are massless, we find that the period matrix is completely specified by [N/2] effective couplings. On each of these, we show that the S-duality group acts as a generalized triangle group and that its hauptmodul can be used to write a non-perturbatively exact relation between each effective coupling and the bare one. For N = 2, 3, 4 and 6, the generalized triangle group is an arithmetic Hecke group which contains a subgroup that is also a congruence subgroup of the modular group PSL(2,Z). For these cases, we introduce mass deformations that respect the symmetries of the special vacuum and show that the constraints arising from S-duality make it possible to resum the instanton contributions to the period matrix in terms of meromorphic modular forms which solve modular anomaly equations.

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arXiv2016

Resumming instantons in N=2* theories with arbitrary gauge groups

We discuss the modular anomaly equation satisfied by the the prepotential of 4-dimensional N=2* theories and show that its validity is related to S-duality. The recursion relations that follow from the modular anomaly equation allow one to write the prepotential in terms of (quasi)-modular forms, thus resumming the instanton contributions. These results can be checked against the microscopic multi-instanton calculus in the case of classical algebras, but are valid also for the exceptional E6, E7, E8, F4 and G2 algebras, where direct computations are not available.

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arXiv2015

S-duality and the prepotential in N=2* theories (I): the ADE algebras

The prepotential of N=2* supersymmetric theories with unitary gauge groups in an Omega-background satisfies a modular anomaly equation that can be recursively solved order by order in an expansion for small mass. By requiring that S-duality acts on the prepotential as a Fourier transform we generalise this result to N=2* theories with gauge algebras of the D and E type and show that their prepotentials can be written in terms of quasi-modular forms of SL(2,Z). The results are checked against microscopic multi-instanton calculus based on localization for the A and D series and reproduce the known 1-instanton prepotential of the pure N=2 theories for any gauge group of ADE type. Our results can also be used to obtain the multi-instanton terms in the exceptional theories for which the microscopic instanton calculus and the ADHM construction are not available.

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arXiv2015

S-duality and the prepotential in N=2* theories (II): the non-simply laced algebras

We derive a modular anomaly equation satisfied by the prepotential of the N=2* supersymmetric theories with non-simply laced gauge algebras, including the classical B and C infinite series and the exceptional F4 and G2 cases. This equation determines the exact prepotential recursively in an expansion for small mass in terms of quasi-modular forms of the S-duality group. We also discuss the behaviour of these theories under S-duality and show that the prepotential of the SO(2r+1) theory is mapped to that of the Sp(2r) theory and viceversa, while the exceptional F4 and G2 theories are mapped into themselves (up to a rotation of the roots) in analogy with what happens for the N=4 supersymmetric theories. These results extend the analysis for the simply laced groups presented in a companion paper.

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arXiv2015

Modular anomaly equations and S-duality in N=2 conformal SQCD

We use localization techniques to study the non-perturbative properties of an N=2 superconformal gauge theory with gauge group SU(3) and six fundamental flavours. The instanton corrections to the prepotential, the dual periods and the period matrix are calculated in a locus of special vacua possessing a Z_3 symmetry. In a semi-classical expansion, we show that these observables are constrained by S-duality via a modular anomaly equation which takes the form of a recursion relation. The solutions of the recursion relation are quasi-modular functions of Gamma_1(3), which is a subgroup of the S-duality group and is also a congruence subgroup of SL(2,Z).

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arXiv2015

Non-perturbative studies of N=2 conformal quiver gauge theories

We study N=2 super-conformal field theories in four dimensions that correspond to mass-deformed linear quivers with n gauge groups and (bi-)fundamental matter. We describe them using Seiberg-Witten curves obtained from an M-theory construction and via the AGT correspondence. We take particular care in obtaining the detailed relation between the parameters appearing in these descriptions and the physical quantities of the quiver gauge theories. This precise map allows us to efficiently reconstruct the non-perturbative prepotential that encodes the effective IR properties of these theories. We give explicit expressions in the cases n=1,2, also in the presence of an Omega-background in the Nekrasov-Shatashvili limit. All our results are successfully checked against those of the direct microscopic evaluation of the prepotential a la Nekrasov using localization methods.

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arXiv2014

Modular anomaly equations in N=2* theories and their large-N limit

We propose a modular anomaly equation for the prepotential of the N=2* super Yang-Mills theory on R^4 with gauge group U(N) in the presence of an Omega-background. We then study the behaviour of the prepotential in a large-N limit, in which N goes to infinity with the gauge coupling constant kept fixed. In this regime instantons are not suppressed. We focus on two representative choices of gauge theory vacua, where the vacuum expectation values of the scalar fields are distributed either homogeneously or according to the Wigner semi-circle law. In both cases we derive an all-instanton exact formula for the prepotential. As an application, we show that the gauge theory partition function on S^4 at large N localises around a Wigner distribution for the vacuum expectation values leading to a very simple expression in which the instanton contribution becomes independent of the coupling constant.

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arXiv2013

Modular anomaly equation, heat kernel and S-duality in N=2 theories

We investigate epsilon-deformed N=2 superconformal gauge theories in four dimensions, focusing on the N=2* and Nf=4 SU(2) cases. We show how the modular anomaly equation obeyed by the deformed prepotential can be efficiently used to derive its non-perturbative expression starting from the perturbative one. We also show that the modular anomaly equation implies that S-duality is implemented by means of an exact Fourier transform even for arbitrary values of the deformation parameters, and then we argue that it is possible, perturbatively in the deformation, to choose appropriate variables such that it reduces to a Legendre transform.

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arXiv2012

Non-perturbative gauge/gravity correspondence in N=2 theories

We derive the exact supergravity profile for the twisted scalar field emitted by a system of fractional D3 branes at a Z2 orbifold singularity supporting N=2 quiver gauge theories with unitary groups and bifundamental matter. At the perturbative level this twisted field is "dual" to the gauge coupling but it is corrected non-perturbatively by an infinite tower of fractional D-instantons. The explicit microscopic description allows to derive the gravity profile from disk amplitudes computing the emission rate of the twisted scalar field in terms of chiral correlators in the dual gauge theory. We compute these quantum correlators using multi-instanton localization techniques and/or Seiberg-Witten analysis. Finally, we discuss a non-perturbative relation between the twisted scalar and the effective coupling of the gauge theory for some simple choices of the brane set ups.

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arXiv2008

Non-perturbative effective interactions from fluxes

Motivated by possible implications on the problem of moduli stabilization and other phenomenological aspects, we study D-brane instanton effects in flux compactifications. We focus on a local model and compute non-perturbative interactions generated by gauge and stringy instantons in a N = 1 quiver theory with gauge group U(N_0) x U(N_1) and matter in the bifundamentals. This model is engineered with fractional D3-branes at a C^3/(Z_2 x Z_2) singularity, and its non-perturbative sectors are described by introducing fractional D-instantons. We find a rich variety of instanton-generated F- and D-term interactions, ranging from superpotentials and Beasley-Witten like multi-fermion terms to non-supersymmetric flux-induced instanton interactions.

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