arXiv subjects

Luca Griguolo

Publications and source records attributed to Luca Griguolo.

53 records · Page 3Linked to original sources

arXiv2012

Correlators of Hopf Wilson loops in the AdS/CFT correspondence

We study at quantum level correlators of supersymmetric Wilson loops with contours lying on Hopf fibers of $S^3$. In $\mathcal{N}=4$ SYM theory the strong coupling analysis can be performed using the AdS/CFT correspondence and a connected classical string surface, linking two different fibers, is presented. More precisely, the string solution describes oppositely oriented fibers with the same scalar coupling and depends on an angular parameter, interpolating between a non-BPS configuration and a BPS one. The system can be thought as an alternative deformation of the ordinary antiparallel lines giving the static quark-antiquark potential, that is indeed correctly reproduced, at weak and strong coupling, as the fibers approach one another.

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arXiv2012

Impure Aspects of Supersymmetric Wilson Loops

We study a general class of supersymmetric Wilson loops operator in N = 4 super Yang-Mills theory, obtained as orbits of conformal transformations. These loops are the natural generalization of the familiar circular Wilson-Maldacena operator and their supersymmetric properties are encoded into a Killing spinor that is not pure. We present a systematic analysis of their scalar couplings and of the preserved supercharges, modulo the action of the global symmetry group, both in the compact and in the non-compact case. The quantum behavior of their expectation value is also addressed, in the simplest case of the Lissajous contours: explicit computations at weak-coupling, through Feynman diagrams expansion, and at strong-coupling, by means of AdS/CFT correspondence, suggest the possibility of an exact evaluation.

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arXiv2009

Correlators of supersymmetric Wilson loops at weak and strong coupling

We continue our study of the correlators of a recently discovered family of BPS Wilson loops in N=4 supersymmetric U(N) Yang-Mills theory. We perform explicit computations at weak coupling by means of analytical and numerical methods finding agreement with the exact formula derived from localization. In particular we check the localization prediction at order g^6 for different BPS "latitude" configurations, the N=4 perturbative expansion reproducing the expected results within a relative error of 10^(-4). On the strong coupling side we present a supergravity evaluation of the 1/8 BPS correlator in the limit of large separation, taking into account the exchange of all relevant modes between the string world-sheets. While reproducing the correct geometrical dependence, we find that the associated coefficient does not match the localization result.

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arXiv2008

Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality

We consider aspects of Chern-Simons theory on L(p,q) lens spaces and its relation with matrix models and topological string theory on Calabi-Yau threefolds, searching for possible new large N dualities via geometric transition for non-SU(2) cyclic quotients of the conifold. To this aim we find, on one hand, some novel matrix integral representations of the SU(N) CS partition function in a generic flat background for the whole L(p,q) family and provide a solution for its large N dynamics; on the other, we perform in full detail the construction of a family of would-be dual closed string backgrounds via conifold geometric transition from T^*L(p,q). We can then explicitly prove that Gopakumar-Vafa duality in a fixed vacuum fails in the case q>1, and briefly discuss how it could be restored in a non-perturbative setting.

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arXiv2008

Supersymmetric Wilson loops at two loops

We study the quantum properties of certain BPS Wilson loops in ${\cal N}=4$ supersymmetric Yang-Mills theory. They belong to a general family, introduced recently, in which the addition of particular scalar couplings endows generic loops on $S^3$ with a fraction of supersymmetry. When restricted to $S^2$, their quantum average has been further conjectured to be exactly computed by the matrix model governing the zero-instanton sector of YM$_2$ on the sphere. We perform a complete two-loop analysis on a class of cusped Wilson loops lying on a two-dimensional sphere, finding perfect agreement with the conjecture. The perturbative computation reproduces the matrix-model expectation through a highly non-trivial interplay between ladder diagrams and self-energies/vertex contributions, suggesting the existence of a localization procedure.

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arXiv2007

Thermodynamics of theories with sixteen supercharges in non-trivial vacua

We study the thermodynamics of maximally supersymmetric U(N) Yang-Mills theory on $\mathds{R}\times S^2$ at large $N$. The model arises as a consistent truncation of ${\cal N}=4$ super Yang-Mills on $\mathds{R}\times S^3$ and as the continuum limit of the plane-wave matrix model expanded around the $N$ spherical membrane vacuum. The theory has an infinite number of classical BPS vacua, labeled by a set of monopole numbers, described by dual supergravity solutions. We first derive the Lagrangian and its supersymmetry transformations as a deformation of the usual dimensional reduction of ${\cal N}=1$ gauge theory in ten dimensions. Then we compute the partition function in the zero 't Hooft coupling limit in different monopole backgrounds and with chemical potentials for the $R$-charges. In the trivial vacuum we observe a first-order Hagedorn transition separating a phase in which the Polyakov loop has vanishing expectation value from a regime in which this order parameter is non-zero, in analogy with the four-dimensional case. The picture changes in the monopole vacua due to the structure of the fermionic effective action. Depending on the regularization procedure used in the path integral, we obtain two completely different behaviors, triggered by the absence or the appearance of a Chern-Simons term. In the first case we still observe a first-order phase transition, with Hagedorn temperature depending on the monopole charges. In the latter the large $N$ behavior is obtained by solving a unitary multi-matrix model with a peculiar logarithmic potential, the system does not present a phase transition and it always appears in a ``deconfined'' phase.

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arXiv2007

Phase transitions, double-scaling limit, and topological strings

Topological strings on Calabi--Yau manifolds are known to undergo phase transitions at small distances. We study this issue in the case of perturbative topological strings on local Calabi--Yau threefolds given by a bundle over a two-sphere. This theory can be regarded as a q--deformation of Hurwitz theory, and it has a conjectural nonperturbative description in terms of q--deformed 2d Yang--Mills theory. We solve the planar model and find a phase transition at small radius in the universality class of 2d gravity. We give strong evidence that there is a double--scaled theory at the critical point whose all genus free energy is governed by the Painlevé I equation. We compare the critical behavior of the perturbative theory to the critical behavior of its nonperturbative description, which belongs to the universality class of 2d supergravity. We also give evidence for a new open/closed duality relating these Calabi--Yau backgrounds to open strings with framing.

hep-th↗

arXiv2006

Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory

We study the relationship between instanton counting in N=4 Yang-Mills theory on a generic four-dimensional toric orbifold and the semi-classical expansion of q-deformed Yang-Mills theory on the blowups of the minimal resolution of the orbifold singularity, with an eye to clarifying the recent proposal of using two-dimensional gauge theories to count microstates of black holes in four dimensions. We describe explicitly the instanton contributions to the counting of D-brane bound states which are captured by the two-dimensional gauge theory. We derive an intimate relationship between the two-dimensional Yang-Mills theory and Chern-Simons theory on generic Lens spaces, and use it to show that the correct instanton counting is only reproduced when the Chern-Simons contributions are treated as non-dynamical boundary conditions in the D4-brane gauge theory. We also use this correspondence to discuss the counting of instantons on higher genus ruled Riemann surfaces.

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arXiv2005

Topological strings and large N phase transitions I: Nonchiral expansion of q-deformed Yang-Mills theory

We examine the problem of counting bound states of BPS black holes on local Calabi-Yau threefolds which are fibrations over a Riemann surface by computing the partition function of q-deformed Yang-Mills theory on the Riemann surface. We study in detail the genus zero case and 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. The correspondence between two and three dimensional gauge theories is elucidated by an explicit mapping between two-dimensional Yang-Mills instantons and flat connections on the Lens space. In the large $N$ limit we find a peculiar phase structure in the model. At weak string coupling the theory reduces exactly to the trivial flat connection sector with instanton contributions exponentially suppressed, and the topological string partition function on the resolved conifold is reproduced in this regime. At a certain critical point all non-trivial vacua contribute, instantons are enhanced and the theory appears to undergo a phase transition into a strong coupling regime. We rederive these results by performing a saddle-point approximation to the exact partition function. We obtain a q-deformed version of the Douglas-Kazakov equation for two-dimensional Yang-Mills theory on the sphere, whose one-cut solution below the transition point reproduces the resolved conifold geometry. Above the critical point we propose a two-cut solution that should reproduce the chiral-antichiral dynamics found for black holes on the Calabi-Yau threefold and the Gross-Taylor string in the undeformed limit.

hep-th↗

arXiv2005

Topological strings and large N phase transitions II: Chiral expansion of q-deformed Yang-Mills theory

We continue our study of the large N phase transition in q-deformed Yang-Mills theory on the sphere and its role in connecting topological strings to black hole entropy. We study in detail the chiral theory defined in terms of uncoupled single U(N) representations at large N and write down the resulting partition function by means of the topological vertex. The emergent toric geometry has three Kaehler parameters, one of which corresponds to the expected fibration over the sphere. By taking a suitable double-scaling limit we recover the chiral Gross-Taylor string expansion. To analyse the phase transition we construct a matrix model which describes the chiral gauge theory. It has three distinct phases, one of which should be described by the closed topological string expansion. We verify this expectation by explicit comparison between the matrix model and the chiral topological string free energies. We also show that the critical point in the pertinent phase of the matrix model corresponds to a divergence of the topological string perturbation series.

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arXiv2005

Morita Duality and Noncommutative Wilson Loops in Two Dimensions

We describe a combinatorial approach to the analysis of the shape and orientation dependence of Wilson loop observables on two-dimensional noncommutative tori. Morita equivalence is used to map the computation of loop correlators onto the combinatorics of non-planar graphs. Several nonperturbative examples of symmetry breaking under area-preserving diffeomorphisms are thereby presented. Analytic expressions for correlators of Wilson loops with infinite winding number are also derived and shown to agree with results from ordinary Yang-Mills theory.

hep-th↗

arXiv2004

Instantons, Fluxons and Open Gauge String Theory

We use the exact instanton expansion to illustrate various string characteristics of noncommutative gauge theory in two dimensions. We analyse the spectrum of the model and present some evidence in favour of Hagedorn and fractal behaviours. The decompactification limit of noncommutative torus instantons is shown to map in a very precise way, at both the classical and quantum level, onto fluxon solutions on the noncommutative plane. The weak-coupling singularities of the usual Gross-Taylor string partition function for QCD on the torus are studied in the instanton representation and its double scaling limit, appropriate for the mapping onto noncommutative gauge theory, is shown to be a generating function for the volumes of the principal moduli spaces of holomorphic differentials. The noncommutative deformation of this moduli space geometry is described and appropriate open string interpretations are proposed in terms of the fluxon expansion.

hep-th↗

arXiv2004

Non-commutative topologically massive gauge theory

We investigate the perturbative dynamics of noncommutative topologically massive gauge theories with softly broken supersymmetry. The deformed dispersion relations induced by noncommutativity are derived and their implications on the quantum consistency of the theory are discussed.

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arXiv2003

Classical Solutions of the TEK Model and Noncommutative Instantons in Two Dimensions

The twisted Eguchi-Kawai (TEK) model provides a non-perturbative definition of noncommutative Yang-Mills theory: the continuum limit is approached at large $N$ by performing suitable double scaling limits, in which non-planar contributions are no longer suppressed. We consider here the two-dimensional case, trying to recover within this framework the exact results recently obtained by means of Morita equivalence. We present a rather explicit construction of classical gauge theories on noncommutative toroidal lattice for general topological charges. After discussing the limiting procedures to recover the theory on the noncommutative torus and on the noncommutative plane, we focus our attention on the classical solutions of the related TEK models. We solve the equations of motion and we find the configurations having finite action in the relevant double scaling limits. They can be explicitly described in terms of twist-eaters and they exactly correspond to the instanton solutions that are seen to dominate the partition function on the noncommutative torus. Fluxons on the noncommutative plane are recovered as well. We also discuss how the highly non-trivial structure of the exact partition function can emerge from a direct matrix model computation. The quantum consistency of the TEK formulation is eventually checked by computing Wilson loops in a particular limit.

hep-th↗

arXiv2001

Hard Non-commutative Loops Resummation

The non-commutative version of the euclidean $g^2ϕ^4$ theory is considered. By using Wilsonian flow equations the ultraviolet renormalizability can be proved to all orders in perturbation theory. On the other hand, the infrared sector cannot be treated perturbatively and requires a resummation of the leading divergencies in the two-point function. This is analogous to what is done in the Hard Thermal Loops resummation of finite temperature field theory. Next-to-leading order corrections to the self-energy are computed, resulting in $O(g^3)$ contributions in the massless case, and $O(g^6\log g^2)$ in the massive one.

hep-th↗

arXiv2001

Wilsonian Renormalization Group and the Non-Commutative IR/UV Connection

We study the IR/UV connection of the four-dimensional non-commutative phi^4 theory by using the Wilsonian Renormalization Group equation. Extending the usual formulation to the non-commutative case we are able to prove UV renormalizability to all orders in perturbation theory. The full RG equations are finite in the IR, but perturbative approximations of them are plagued by IR divergences. The latter can be systematically resummed in a way analogous to what is done in finite temperature field theory. As an application, next-to-leading order corrections to the two-point function are explicitly computed. The usual Wilsonian picture, i.e. the insensitivity of the IR regime to the UV, does not hold in the non-commutative case. Nevertheless it can be partially recovered by a matching procedure, in which a high-energy theory, defined in the deep non-commutative regime, is connected at some intermediate scale to a commutative low-energy theory. The latter knows about non-commutativity only through the boundary conditions for two would-be irrelevant couplings.

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arXiv1993

Covariant Anomalies and Functional Determinants

We analize the algebraic structure of consistent and covariant anomalies in gauge and gravitational theories: using a complex extension of the Lie algebra it is possible to describe them in a unified way. Then we study their representations by means of functional determinants, showing how the algebraic solution determines the relevant operators for the definition of the effective action. Particular attention is devoted to the Lorentz anomaly: we obtain by functional methods the covariant anomaly for the spin-current and for the energy-momentum tensor in presence of a curved background. With regard to the consistent sector we are able to give a general functional solution only for $d=2$: using the characterization derived from the extended algebra, we find a continuous family of operators whose determinant describes the effective action of chiral spinors in curved space. We compute this action and we generalize the result in presence of a $U(1)$ gauge connection. Accepted for publication in Fortschritte der Physik.

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