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L. Griguolo

Publications and source records attributed to L. Griguolo.

At least 19 recordsLinked to original sources
arXiv2025

Correlators in non-conformal $\mathcal{N}=2$ gauge theories from localization

We study two-point correlation functions of chiral/anti-chiral operators in SU(N) $\mathcal{N}=2$ gauge theories with massless hyper-multiplets in a representation $\mathcal{R}$ associated with a non-vanishing $\beta$-function. Using supersymmetric localization on the four-sphere $S^4$, these observables can be evaluated by matrix correlators of normal ordered operators. We show that, within a specific regime of validity, standard perturbative calculations based on Feynman diagrams and renormalization procedures in flat space perfectly match the localization predictions up to two loops generalizing and extending previous results. Our analysis highlights that non-trivial interference effects between evanescent terms and the UV poles of the bare coupling are essential for the agreement. On the matrix model side, we employ a direct diagrammatic procedure akin to the Feynman diagram expansion on the field theory description; this simplifies the comparison for generic operators and general matter representation $\mathcal{R}$.

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arXiv2023

Remarks on BPS Wilson loops in non-conformal N=2 gauge theories and localization

We consider 1/2 BPS supersymmetric circular Wilson loops in four-dimensional N=2 SU(N) SYM theories with massless matter content and non-vanishing beta-function. Following Pestun's approach, we can use supersymmetric localization on the sphere S4 to map these observables into a matrix model, provided that the one-loop determinants are consistently regularized. Employing a suitable procedure, we construct the regularized matrix model for these theories and show that, at order g^4, the predictions for the 1/2 BPS Wilson loop match standard perturbative renormalization based on the direct evaluation of Feynman diagrams on S4. Despite conformal symmetry begin broken at the quantum level, we also demonstrate that the matrix model approaches perfectly captures the expression of the renormalized observable in flat space at this perturbative order. Moreover, we revisit in detail the difference theory approach, showing that when the beta-function is non-vanishing, this method does not account for evanescent terms which are made finite by the renormalization procedure and participate to the corrections at order g^6.

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arXiv2019

Circular Wilson loops in defect ${\cal N}$=4 SYM: phase transitions, double-scaling limits and OPE expansion

We consider circular Wilson loops in a defect version of $\mathcal{N}=4$ super-Yang-Mills theory which is dual to the D3-D5 brane system with $k$ units of flux. When the loops are parallel to the defect, we can construct both BPS and non-BPS operators, depending on the orientation of the scalar couplings in the R-symmetry directions. At strong 't Hooft coupling we observe, in the non supersymmetric case, a Gross-Ooguri-like phase transition in the dual gravitational theory: the familiar disk solution dominates, as expected, when the operator is far from the defect while a cylindrical string worldsheet, connecting the boundary loop with the probe D5-brane, is favourite below a certain distance (or equivalently for large radii of the circles). In the BPS case, instead, the cylindrical solution does not exist for any choice of the physical parameters, suggesting that the exchange of light supergravity modes always saturate the expectation value at strong coupling. We study the double-scaling limit for large $k$ and large 't Hooft coupling, finding full consistency in the non-BPS case between the string solution and the one-loop perturbative result. Finally we discuss, in the BPS case, the failure of the double-scaling limit and the OPE expansion of the Wilson loop, finding consistency with the known results for the one-point functions of scalar composite operators.

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arXiv2016

Precision calculation of 1/4-BPS Wilson loops in AdS$_5\times S^5$

We study the strong coupling behaviour of $1/4$-BPS circular Wilson loops (a family of "latitudes") in ${\cal N}=4$ Super Yang-Mills theory, computing the one-loop corrections to the relevant classical string solutions in AdS$_5\times$S$^5$. Supersymmetric localization provides an exact result that, in the large 't Hooft coupling limit, should be reproduced by the sigma-model approach. To avoid ambiguities due to the absolute normalization of the string partition function, we compare the $ratio$ between the generic latitude and the maximal 1/2-BPS circle: Any measure-related ambiguity should simply cancel in this way. We use Gel'fand-Yaglom method to calculate the relevant functional determinants, that present some complications with respect to the standard circular case. After a careful numerical evaluation of our final expression we still find disagreement with the localization answer: The difference is encoded into a precise "remainder function". We comment on the possible origin and resolution of this discordance.

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arXiv2015

Remarks on the geometrical properties of semiclassically quantized strings

We discuss some geometrical aspects of the semiclassical quantization of string solutions in Type IIB Green-Schwarz action on $\ads_5\times \sphere^5$. We concentrate on quadratic fluctuations around classical configurations, expressing the relevant differential operators in terms of (intrinsic and extrinsic) invariants of the background geometry. The aim of our exercises is to present some compact expressions encoding the spectral properties of bosonic and fermionic fluctuations. The appearing of non-trivial structures on the relevant bundles and their role in concrete computations are also considered. We corroborate the presentation of general formulas by working out explicitly a couple of relevant examples, namely the spinning string and the latitude BPS Wilson loop.

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arXiv2012

New supersymmetric Wilson loops in ABJ(M) theories

We present two new families of Wilson loop operators in N= 6 supersymmetric Chern-Simons theory. The first one is defined for an arbitrary contour on the three dimensional space and it resembles the Zarembo's construction in N=4 SYM. The second one involves arbitrary curves on the two dimensional sphere. In both cases one can add certain scalar and fermionic couplings to the Wilson loop so it preserves at least two supercharges. Some previously known loops, notably the 1/2 BPS circle, belong to this class, but we point out more special cases which were not known before. They could provide further tests of the gauge/gravity correspondence in the ABJ(M) case and interesting observables, exactly computable by localization

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arXiv2009

Correlators of supersymmetric Wilson-loops, protected operators and matrix models in N=4 SYM

We study the correlators of a recently discovered family of BPS Wilson loops in ${\cal N}=4$ supersymmetric U(N) Yang-Mills theory. When the contours lie on a two-sphere in the space-time, we propose a closed expression that is valid for all values of the coupling constant $g$ and for any rank $N$, by exploiting the suspected relation with two-dimensional gauge theories. We check this formula perturbatively at order ${\cal O}(g^4)$ for two latitude Wilson loops and we show that, in the limit where one of the loops shrinks to a point, logarithmic corrections in the shrinking radius are absent at ${\cal O}(g^6)$. This last result strongly supports the validity of our general expression and suggests the existence of a peculiar protected local operator arising in the OPE of the Wilson loop. At strong coupling we compare our result to the string dual of the ${\cal N}=4$ SYM correlator in the limit of large separation, presenting some preliminary evidence for the agreement.

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arXiv2006

Topological Strings, Two-Dimensional Yang-Mills Theory and Chern-Simons Theory on Torus Bundles

We study the relations between two-dimensional Yang-Mills theory on the torus, topological string theory on a Calabi-Yau threefold whose local geometry is the sum of two line bundles over the torus, and Chern-Simons theory on torus bundles. The chiral partition function of the Yang-Mills gauge theory in the large N limit is shown to coincide with the topological string amplitude computed by topological vertex techniques. We use Yang-Mills theory as an efficient tool for the computation of Gromov-Witten invariants and derive explicitly their relation with Hurwitz numbers of the torus. We calculate the Gopakumar-Vafa invariants, whose integrality gives a non-trivial confirmation of the conjectured nonperturbative relation between two-dimensional Yang-Mills theory and topological string theory. We also demonstrate how the gauge theory leads to a simple combinatorial solution for the Donaldson-Thomas theory of the Calabi-Yau background. We match the instanton representation of Yang-Mills theory on the torus with the nonabelian localization of Chern-Simons gauge theory on torus bundles over the circle. We also comment on how these results can be applied to the computation of exact degeneracies of BPS black holes in the local Calabi-Yau background.

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arXiv2005

Black-holes, topological strings and large N phase transitions

The counting of microstates of BPS black-holes on local Calabi-Yau of the form ${\mathcal O}(p-2)\oplus{\mathcal O}(-p) \longrightarrow S^2$ is explored by computing the partition function of q-deformed Yang-Mills theory on $S^2$. We obtain, at finite $N$, the instanton expansion of the gauge theory. It can be written exactly as the partition function for U(N) Chern-Simons gauge theory on a Lens space, summed over all non-trivial vacua, plus a tower of non-perturbative instanton contributions. In the large $N$ limit we find a peculiar phase structure in the model. At weak string coupling the theory reduces to the trivial sector and the topological string partition function on the resolved conifold is reproduced in this regime. At a certain critical point, instantons are enhanced and the theory undergoes a phase transition into a strong coupling regime. The transition from the strong coupling phase to the weak coupling phase is of third order.

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arXiv2004

Two-Dimensional Yang-Mills Theory and Moduli Spaces of Holomorphic Differentials

We describe and solve a double scaling limit of large N Yang-Mills theory on a two-dimensional torus. We find the exact strong-coupling expansion in this limit and describe its relation to the conventional Gross-Taylor series. The limit retains only the chiral sector of the full gauge theory and the coefficients of the expansion determine the asymptotic Hurwitz numbers, in the limit of infinite winding number, for simple branched coverings of a torus. These numbers are computed exactly from the gauge theory vacuum amplitude and shown to coincide with the volumes of the principal moduli spaces of holomorphic differentials. The string theory interpretation of the double scaling limit is also described.

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arXiv2002

Large Gauge Invariance in NonAbelian Finite Temperature Effective Actions

We analyze large gauge invariance in combined nonabelian and thermal QFT and their physical consequences for D=3 effective actions. After briefly reviewing the structure of bundles and large gauge transformations that arise in non-simply connected 3-manifolds and gauge groups, we discuss their connections to Chern-Simons terms and Wilson-Polyakov loops. We then provide an invariant characterization of the ``abelian'' fluxes encountered in explicit computations of finite temperature effective actions. In particular we relate, and provide explicit realizations of, these fluxes to a topological index that measures the obstruction to global diagonalization of the loops around compactified time. We also explore the fate of, and exhibit some everywhere smooth, large transformations for non-vanishing index in various topologies.

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arXiv2001

Towards the solution of noncommutative $YM_2$: Morita equivalence and large N-limit

In this paper we shall investigate the possibility of solving U(1) theories on the non-commutative (NC) plane for arbitrary values of $θ$ by exploiting Morita equivalence. This duality maps the NC U(1) on the two-torus with a rational parameter $θ$ to the standard U(N) theory in the presence of a 't Hooft flux, whose solution is completely known. Thus, assuming a smooth dependence on $θ$, we are able to construct a series rational approximants of the original theory, which is finally reached by taking the large $N-$limit at fixed 't Hooft flux. As we shall see, this procedure hides some subletities since the approach of $N$ to infinity is linked to the shrinking of the commutative two-torus to zero-size. The volume of NC torus instead diverges and it provides a natural cut-off for some intermediate steps of our computation. In this limit, we shall compute both the partition function and the correlator of two Wilson lines. A remarkable fact is that the configurations, providing a finite action in this limit, are in correspondence with the non-commutative solitons (fluxons) found independently by Polychronakos and by Gross and Nekrasov, through a direct computation on the plane.

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arXiv2001

On the unitarity of quantum gauge theories on non-commutative spaces

We study the perturbative unitarity of non-commutative quantum Yang-Mills theories, extending previous investigations on scalar field theories to the gauge case where non-locality mingles with the presence of unphysical states. We concentrate our efforts on two different aspects of the problem. We start by discussing the analytical structure of the vacuum polarization tensor, showing how Cutkoski's rules and positivity of the spectral function are realized when non-commutativity does not affect the temporal coordinate. When instead non-commutativity involves time, we find the presence of extra troublesome singularities on the $p_0^2$-plane that seem to invalidate the perturbative unitarity of the theory. The existence of new tachyonic poles, with respect to the scalar case, is also uncovered. Then we turn our attention to a different unitarity check in the ordinary theories, namely time exponentiation of a Wilson loop. We perform a $O(g^4)$ generalization to the (spatial) non-commutative case of the familiar results in the usual Yang-Mills theory. We show that exponentiation persists at $O(g^4)$ in spite of the presence of Moyal phases reflecting non-commutativity and of the singular infrared behaviour induced by UV/IR mixing.

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arXiv2001

The structure of radiatively induced Lorentz and CPT violation in QED at finite temperature

We obtain the induced Lorentz- and CPT-violating term in QED at finite temperature using imaginary-time formalism and dimensional regularization. Its form resembles a Chern-Simons-like structure, but, unexpectedly, it does not depend on the temporal component of the fixed $b_μ$ constant vector that is coupled to the axial current. Nevertheless Ward identities are respected and its coefficient vanishes at T=0, consistently with previous computations with the same regularization procedure, and it is a non-trivial function of temperature. We argue that at finite $T$ a Chern-Simons-like Lorentz- and CPT-violating term is generically present, the value of its coefficient being unambiguously determined up to a $T-$independent constant, related to the zero-temperature renormalization conditions.

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arXiv2000

Multiple vacua in two-dimensional Yang-Mills theory

Two-dimensional SU(N) Yang-Mills theory is endowed with a non-trivial vacuum structure (k-sectors). The presence of k-sectors modifies the energy spectrum of the theory and its instanton content, the (Euclidean) space-time being compactified on a sphere. For the exact solution, in the limit in which the sphere is decompactified, a k-sector can be mimicked by the presence of k-fundamental charges at infinity, according to a Witten's suggestion. However, this property neither holds before decompactification nor for the genuine perturbative solution which corresponds to the zero-instanton contribution on the sphere.

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arXiv2000

Light-front vacuum and instantons in two dimensions

We review several aspects of Yang-Mills theory (YMT) in two dimensions, related to its perturbative and topological properties. Consistency between light-front and equal-time formulations is thoroughly discussed.

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arXiv2000

Wilson loops in the adjoint representation and multiple vacua in two-dimensional Yang-Mills theory

$QCD_2$ with fermions in the adjoint representation is invariant under $SU(N)/Z_N$ and thereby is endowed with a non-trivial vacuum structure (k-sectors). The static potential between adjoint charges, in the limit of infinite mass, can be therefore obtained by computing Wilson loops in the pure Yang-Mills theory with the same non-trivial structure. When the (Euclidean) space-time is compactified on a sphere $S^2$, Wilson loops can be exactly expressed in terms of an infinite series of topological excitations (instantons). The presence of k-sectors modifies the energy spectrum of the theory and its instanton content. For the exact solution, in the limit in which the sphere is decompactified, a k-sector can be mimicked by the presence of k-fundamental charges at $\infty$, according to a Witten's suggestion. However this property neither holds before decompactification nor for the genuine perturbative solution which corresponds to the zero-instanton contribution on $S^2$.

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