Topological Gauge Theories on Local Spaces and Black Hole Entropy Countings

We study cohomological gauge theories on total spaces of holomorphic line bundles over complex manifolds and obtain their reduction to the base manifold by U(1) equivariant localization of the path integral. We exemplify this general mechanism by proving via exact path integral localization a reduction for local curves conjectured in hep-th/0411280, relevant to the calculation of black hole entropy/Gromov-Witten invariants. Agreement with the four-dimensional gauge theory is recovered by taking into account in the latter non-trivial contributions coming from one-loop fluctuations determinants at the boundary of the total space. We also study a class of abelian gauge theories on Calabi-Yau local surfaces, describing the quantum foam for the A-model, relevant to the calculation of Donaldson-Thomas invariants.Comment: 17 page

Bose-Einstein condensation and superfluidity of a weakly-interacting photon gas in a nonlinear Fabry-Perot cavity

A field theoretical framework for the recently proposed photon condensation effect in a nonlinear Fabry-Perot cavity is discussed. The dynamics of the photon gas turns out to be described by an effective 2D Hamiltonian of a complex massive scalar field. Finite size effects are shown to be relevant for the existence of the photon condensate.Comment: 9 pages, LateX2e, final version to appear in Phys. Lett.

Multi - instantons, supersymmetry and topological field theories

In this letter we argue that instanton-dominated Green's functions in N=2 Super Yang-Mills theories can be equivalently computed either using the so-called constrained instanton method or making reference to the topological twisted version of the theory. Defining an appropriate BRST operator (as a supersymmetry plus a gauge variation), we also show that the expansion coefficients of the Seiberg-Witten effective action for the low-energy degrees of freedom can be written as integrals of total derivatives over the moduli space of self-dual gauge connections

Quantum curves and q-deformed Painlev\ue9 equations

We propose that the grand canonical topological string partition functions satisfy finite-difference equations in the closed string moduli. In the case of genus one mirror curve, these are conjectured to be the q-difference Painlev\ue9 equations as in Sakai\u2019s classification. More precisely, we propose that the tau functions of q-Painlev\ue9 equations are related to the grand canonical topological string partition functions on the corresponding geometry. In the toric cases, we use topological string/spectral theory duality to give a Fredholm determinant representation for the above tau functions in terms of the underlying quantum mirror curve. As a consequence, the zeroes of the tau functions compute the exact spectrum of the associated quantum integrable systems. We provide details of this construction for the local P1 7 P1 case, which is related to q-difference Painlev\ue9 with affine A1 symmetry, to SU(2) Super Yang\u2013Mills in five dimensions and to relativistic Toda system. \ua9 2019, Springer Nature B.V

BPS Quivers of Five-Dimensional SCFTs, Topological Strings and q-Painlevé Equations

We study the discrete flows generated by the symmetry group of the BPS quivers for Calabi–Yau geometries describing five-dimensional superconformal quantum field theories on a circle. These flows naturally describe the BPS particle spectrum of such theories and at the same time generate bilinear equations of q-difference type which, in the rank one case, are q-Painlevé equations. The solutions of these equations are shown to be given by grand canonical topological string partition functions which we identify with τ-functions of the cluster algebra associated to the quiver. We exemplify our construction in the case corresponding to five-dimensional SU(2) pure super Yang–Mills and Nf= 2 on a circle

Counting Yang-Mills Instantons by Surface Operator Renormalization Group Flow

We show that the nonperturbative dynamics of N=2 super-Yang-Mills theories in a self-dual ω background and with arbitrary simple gauge group is fully determined by studying renormalization group equations of vacuum expectation values of surface operators generating one-form symmetries. The corresponding system of equations is a nonautonomous Toda chain, the time being the renormalization group scale. We obtain new recurrence relations which provide a systematic algorithm computing multi-instanton corrections from the tree-level one-loop prepotential as the asymptotic boundary condition of the renormalization group equations. We exemplify by computing the E6 and G2 cases up to two instantons

Four-Dimensional Yang-Mills Theory as a Deformation of Topological BF Theory

The classical action for pure Yang--Mills gauge theory can be formulated as a deformation of the topological $BF$ theory where, beside the two-form field $B$, one has to add one extra-field $\eta$ given by a one-form which transforms as the difference of two connections. The ensuing action functional gives a theory that is both classically and quantistically equivalent to the original Yang--Mills theory. In order to prove such an equivalence, it is shown that the dependency on the field $\eta$ can be gauged away completely. This gives rise to a field theory that, for this reason, can be considered as semi-topological or topological in some but not all the fields of the theory. The symmetry group involved in this theory is an affine extension of the tangent gauge group acting on the tangent bundle of the space of connections. A mathematical analysis of this group action and of the relevant BRST complex is discussed in details.Comment: 74 pages, LaTeX, minor corrections; to be published in Commun. Math. Phy

Romanesque and territory. The construction materials of Sardinian medieval churches: new approaches to the valorization, conservation and restoration

This paper is intended to illustrate a multidisciplinary research project devoted to the study of the constructive materials of the Romanesque churches in Sardinia during the “Giudicati” period (11th -13th centuries). The project focuses on the relationship between a selection of monuments and their territory, both from a historical-architectural perspective and from a more modern perspective addressing future restoration works. The methodologies of the traditional art-historical research (study of bibliographic, epigraphic and archival sources, formal reading of artifacts) are flanked by new technologies: digital surveys executed with a 3D laser-scanner, analyses of the materials (stones, mortars, bricks) with different instrumental methods: X-ray fluorescence (XRF) and inductively coupled mass spectrometry (ICP-MS) for chemical composition, X-ray diffractometer (XRD) to determine the alteration phases (e.g., soluble salts), optical microscopy and electronic (SEM) to study textures, mineral assemblages and microstructures, termogravimetric/differential scanning, calorimetric analysis (TG/DTA) for the composition of the binder mortars. This multidisciplinary approach allows the achieving of important results in an archaeometric context: 1) from a historical point of view, with the possible identification of ancient traffics, trade routes, sources of raw materials, construction phases, wall textures; 2) from a conservative point of view, by studying chemical and physical weathering processes of stone materials compatible for replacement in case of future restoration works. Sardinian Romanesque architectural heritage is particularly remarkable: about 200 churches of different types and sizes, with the almost exclusive use of cut stones. Bi- or poly-chromy, deriving from the use of different building materials, characterizes many of these monuments, becoming also a vehicle for political and cultural meanings. The paper will present some case studies aimed to illustrate the progress of the project and the results achieved