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M. Billo'

Publications and source records attributed to M. Billo'.

At least 19 recordsLinked to original sources
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.

hep-th↗
arXiv2023

Integrated correlators with a Wilson line in $\mathcal{N}=4$ SYM

In the context of integrated correlators in $\mathcal{N}=4$ SYM, we study the 2-point functions of local operators with a superconformal line defect. Starting from the mass-deformed $\mathcal{N}=2^*$ theory in presence of a $\frac{1}{2}$-BPS Wilson line, we exploit the residual superconformal symmetry after the defect insertion, and show that the massive deformation corresponds to integrated insertions of the superconformal primaries belonging to the stress tensor multiplet with a specific integration measure which is explicitly derived after enforcing the superconformal Ward identities. Finally, we show how the Wilson line integrated correlator can be computed by the $\mathcal{N}=2^*$ Wilson loop vacuum expectation value on a 4-sphere in terms of a matrix model using supersymmetric localization. In particular, we reformulate previous matrix model computations by making use of recursion relations and Bessel kernels, providing a direct link with more general localization computations in $\mathcal{N}=2$ theories.

hep-th↗
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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arXiv2010

New results on the effective string corrections to the inter-quark potential

We propose a new approach to the study of the inter-quark potential in Lattice Gauge Theories. Instead of looking at the expectation value of Polyakov loop correlators we study the modifications induced in the chromoelectric flux by the presence of the Polyakov loops. In abelian LGTs, thanks to duality, this study can be performed in a very efficient way, allowing to reach high precision with a reasonable CPU cost. The major advantage of this numerical strategy is that it allows to eliminate the dominant effective string correction to the inter-quark potential (the Luscher term) thus giving an unique opportunity to test higher order corrections. Performing a set of simulations in the 3d gauge Ising model we were thus able to precisely identify and measure both the quartic and the sextic effective string corrections to the inter-quark potential. While the quartic term perfectly agrees with the Nambu-Goto one the sextic term is definitely different. Our result seems to disagree with the recent proof by Aharony and Karzbrun of the universality of the sextic correction. We discuss a few possible explanations of this disagreement. The numerical approach described above can also be applied to the study of Wilson loops. In this case, the numerical results are precise enough to test the two-loop prediction of the Nambu-Goto action. The two-loop NG result computed time ago by by Dietz and Filk is incompatible with the data; however, after correcting some mistakes in their expression, compatibility is restored. The viability of a first-order, operatorial description of the Wilson loop is also pointed out.

hep-lat↗
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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arXiv2001

Fractional branes on ALE orbifolds

We derive the classical type IIB supergravity solution describing fractional D3-branes transverse to a C^2/Gamma orbifold singularity, for Gamma any Kleinian ADE subgroup. This solution fully describes the N=2 gauge theory with appropriate gauge groups and matter living on the branes, up to non-perturbative instanton contributions.

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arXiv2001

Classical geometry and gauge duals for fractional branes on ALE orbifolds

We investigate the classical geometry corresponding to a collection of fractional D3 branes in the orbifold limit of an ALE space. We discuss its interpretation in terms of the world-volume gauge theory on the branes, which is in general a non conformal N=2 Yang-Mills theory with matter. The twisted fields reproduce the perturbative behaviour of the gauge theory. We regulate the IR singularities for both twisted and untwisted fields by means of an enhancon mechanism qualitatively consistent with the gauge theory expectations. The five-form flux decreases logarithmically towards the IR with a coefficient dictated by the gauge theory beta-functions.

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arXiv2001

Branched Coverings and Interacting Matrix Strings in Two Dimensions

We construct the lattice gauge theory of the group G_N, the semidirect product of the permutation group S_N with U(1)^N, on an arbitrary Riemann surface. This theory describes the branched coverings of a two-dimensional target surface by strings carrying a U(1) gauge field on the world sheet. These are the non-supersymmetric Matrix Strings that arise in the unitary gauge quantization of a generalized two-dimensional Yang-Mills theory. By classifying the irreducible representations of G_N, we give the most general formulation of the lattice gauge theory of G_N, which includes arbitrary branching points on the world sheet and describes the splitting and joining of strings.

hep-th↗
arXiv2001

Orbifold boundary states from Cardy's condition

Boundary states for D-branes at orbifold fixed points are constructed in close analogy with Cardy's derivation of consistent boundary states in RCFT. Comments are made on the interpretation of the various coefficients in the explicit expressions, and the relation between fractional branes and wrapped branes is investigated for $\mathbb{C}^2/Γ$ orbifolds. The boundary states are generalised to theories with discrete torsion and a new check is performed on the relation between discrete torsion phases and projective representations.

hep-th↗
arXiv2000

Generalized two-dimensional Yang-Mills theory is a matrix string theory

We consider two-dimensional Yang-Mills theories on arbitrary Riemann surfaces. We introduce a generalized Yang-Mills action, which coincides with the ordinary one on flat surfaces but differs from it in its coupling to two-dimensional gravity. The quantization of this theory in the unitary gauge can be consistently performed taking into account all the topological sectors arising from the gauge-fixing procedure. The resulting theory is naturally interpreted as a Matrix String Theory, that is as a theory of covering maps from a two-dimensional world-sheet to the target Riemann surface.

hep-th↗
arXiv1999

Matrix strings from generalized Yang-Mills theory on arbitrary Riemann surfaces

We quantize pure 2d Yang-Mills theory on an arbitrary Riemann surface in the gauge where the field strength is diagonal. Twisted sectors originate, as in Matrix string theory, from permutations of the eigenvalues around homotopically non-trivial loops. These sectors, that must be discarded in the usual quantization due to divergences occurring when two eigenvalues coincide, can be consistently kept if one modifies the action by introducing a coupling of the field strength to the space-time curvature. This leads to a generalized Yang-Mills theory whose action reduces to the usual one in the limit of zero curvature. After integrating over the non-diagonal components of the gauge fields, the theory becomes a free string theory (sum over unbranched coverings) with a U(1) gauge theory on the world-sheet. This is shown to be equivalent to a lattice theory with a gauge group which is the semi-direct product of S_N and U(1)^N. By using well known results on the statistics of coverings, the partition function on arbitrary Riemann surfaces and the kernel functions on surfaces with boundaries are calculated. Extensions to include branch points and non-abelian groups on the world-sheet are briefly commented upon.

hep-th↗
arXiv1999

2D Yang-Mills Theory as a Matrix String Theory

Quantization of two-dimensional Yang-Mills theory on a torus in the gauge where the field strength is diagonal leads to twisted sectors that are completely analogous to the ones that originate long string states in Matrix String Theory. If these sectors are taken into account the partition function is different from the standard one found in the literature and the invariance of the theory under modular transformations of the torus appears to hold in a stronger sense. The twisted sectors are in one-to-one correspondence with the coverings of the torus without branch points, so they define by themselves a string theory. A possible duality between this string theory and the Gross-Taylor string is discussed, and the problems that one encounters in generalizing this approach to interacting strings are pointed out. This talk is based on a previous paper by the same authors, but it contains some new results and a better interpretation of the results already obtained.

hep-th↗
arXiv1998

Matrix string states in pure 2d Yang Mills theories

We quantize pure 2d Yang-Mills theory on a torus in the gauge where the field strength is diagonal. Because of the topological obstructions to a global smooth diagonalization, we find string-like states in the spectrum similar to the ones introduced by various authors in Matrix string theory. We write explicitly the partition function, which generalizes the one already known in the literature, and we discuss the role of these states in preserving modular invariance. Some speculations are presented about the interpretation of 2d Yang-Mills theory as a Matrix string theory.

hep-th↗
arXiv1998

The Lorentz force between D0 and D6 branes in string and M(atrix) theory

We use different techniques to analyze the system formed by a D0 brane and a D6 brane (with background gauge fields) in relative motion. In particular, using the closed string formalism of boosted boundary states, we show the presence of a term linear in the velocity, corresponding to the Lorentz force experienced by the D0 brane moving in the magnetic background produced by the D6 brane. This term, that was missed in previous analyses of this system, comes entirely from the R-R odd spin structure and is also reproduced by a M(atrix) theory calculation.

hep-th↗
arXiv1998

Microscopic string analysis of the D0-D8 brane system and dual R-R states

Using the boundary state formalism, we perform a microscopic string analysis of the interaction between two D-branes and provide a local interpretation for the R-R force in the D0-D8 brane system. To do so, we construct BRST invariant vertex operators for the massless R-R states in the asymmetric picture that are proportional to potentials rather than field strengths. The Hilbert space of such R-R states contains combinations of two vectors that decouple from all physical amplitudes, even in the presence of boundaries. Identifying these vectors, we remove the null states and recover duality relations among R-R potentials. If we specify to the D0-D8 brane system, this mechanism implies that the R-R 1-form state has a non-zero overlap with both the D0-brane and the D8-brane, thus explaining from a local point of view the non-vanishing R-R contribution in the interaction for the D0-D8 brane system and those related to it by duality.

hep-th↗
arXiv1997

Analytic results in 2+1-dimensional Finite Temperature LGT

In a 2+1-dimensional pure LGT at finite temperature the critical coupling for the deconfinement transition scales as $β_c(n_t) = J_c n_t + a_1$, where $n_t$ is the number of links in the ``time-like'' direction of the symmetric lattice. We study the effective action for the Polyakov loop obtained by neglecting the space-like plaquettes, and we are able to compute analytically in this context the coefficient $a_1$ for any SU(N) gauge group; the value of $J_c$ is instead obtained from the effective action by means of (improved) mean field techniques. Both coefficients have already been calculated in the large N limit in a previous paper. The results are in very good agreement with the existing Monte Carlo simulations. This fact supports the conjecture that, in the 2+1-dimensional theory, space-like plaquettes have little influence on the dynamics of the Polyakov loops in the deconfined phase.

hep-th↗
arXiv1996

A solvable twisted one-plaquette model

We solve a hot twisted Eguchi-Kawai model with only timelike plaquettes in the deconfined phase, by computing the quadratic quantum fluctuations around the classical vacuum. The solution of the model has some novel features: the eigenvalues of the time-like link variable are separated in L bunches, if L is the number of links of the original lattice in the time direction, and each bunch obeys a Wigner semicircular distribution of eigenvalues. This solution becomes unstable at a critical value of the coupling constant, where it is argued that a condensation of classical solutions takes place. This can be inferred by comparison with the heat-kernel model in the hamiltonian limit, and the related Douglas-Kazakov phase transition in QCD2. As a byproduct of our solution, we can reproduce the dependence of the coupling constant from the parameter describing the asymmetry of the lattice, in agreement with previous results by Karsch.

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