arXiv subjects

Antonio Pittelli

Publications and source records attributed to Antonio Pittelli.

18 recordsLinked to original sources

arXiv2026

Localization, Factorization and Dualities for Elliptic Kernels

We study the exact partition function of 4d $\mathcal N=1$ supersymmetric gauge theories on a torus times a cylinder $\mathrm{Cyl}=I\times S^1$, where $I$ is a finite interval carrying two boundary components. Each endpoint supports an independent Dirichlet or Robin-like boundary polarization, so that the partition function is a boundary-to-boundary elliptic kernel. We construct the rigid supersymmetric geometry, determine the BPS locus, and compute the chiral-multiplet 1-loop determinants for the four possible boundary polarizations via equivariant localization. The resulting elementary building blocks are theta functions dressed by cubic phases. We then prove rank-changing Seiberg-type dualities as identities of Jeffrey--Kirwan residues of these elliptic kernels. We also discuss factorization into holomorphic-block cap wavefunctions represented by elliptic Gamma functions, dimensional reductions to three and two dimensions, complete-intersection gauged linear sigma models, and elliptic kernels for 4d $\mathcal N=4$ super Yang--Mills and the Klebanov--Witten theory, useful for holographic applications.

hep-th↗

arXiv2024

Microstates of accelerating and supersymmetric AdS$_4$ black holes from the spindle index

We provide a first principles derivation of the microscopic entropy of a very general class of supersymmetric, rotating and accelerating black holes in AdS$_4$. This is achieved by analysing the large-$N$ limit of the spindle index and completes the construction of the first example of a holographic duality involving supersymmetric field theories defined on orbifolds with conical singularities.

hep-th↗

arXiv2024

Orbifold Indices in Four Dimensions

We introduce supersymmetric indices for four-dimensional gauge theories defined on $\mathscr O \times S^1$, where $\mathscr O $ is a circle bundle over the weighted complex projective line informally known as spindle. Trivial fibrations yield a four-dimensional version of the spindle index, which we obtain by applying localization to partition functions of theories on the direct product of a spindle and a two-dimensional torus. Conversely, non-trivial fibrations lead to the branched lens index, which we compute by localizing theories on the direct product of a circle and a branched covering of the lens space, possibly endowed with conical singularities. The branched lens index encompasses the maximally refined four-dimensional lens index as a special case.

hep-th↗

arXiv2024

Symmetry Restoration and Uniformly Accelerated Observers in Minkowski Spacetime

We reassess the problem of symmetry restoration induced by observers' acceleration within the context of interacting quantum field theories in Minkowski spacetime. We argue that the imposition of a frame-independent renormalization condition negates any observed symmetry restoration by a Rindler observer. Technically, we compute the one-loop effective potential of a $\lambda\varphi^4$ theory for an accelerated observer, employing a distinct methodology from prior investigations. Emphasizing the intricacies of the model's renormalization, the analysis offers novel insights into the interplay between acceleration and spontaneous symmetry breaking in quantum field theory.

hep-th↗

arXiv2023

Supersymmetry and Localization on Three-Dimensional Orbifolds

We consider three-dimensional ${\mathcal N}=2$ supersymmetric field theories defined on general complex-valued backgrounds of Euclidean new minimal supergravity admitting two Killing spinors of opposite $R$-charges. We compute partition functions for theories defined on general circle bundles over spindles $\Sigma $, including $\Sigma \times S^1$ as well as branched and squashed lens spaces, thus obtaining novel observables characterizing three-dimensional supersymmetric gauge theories. We discuss both twisted and anti-twisted theories compactified on $\Sigma \times S^1$ and demonstrate that their partition functions are encoded by a single formula that we refer to as the \emph{spindle index}, unifying and generalizing superconformal and topologically twisted indices in the limit where orbifold singularities are absent. Furthermore, we test our new index using non-perturbative dualities and obtain one-loop determinants of two-dimensional supersymmetric gauge theories compactified on the spindle.

hep-th↗

arXiv2023

Twisted Index on Hyperbolic Four-Manifolds

We introduce the topologically twisted index for four-dimensional $\mathcal N=1$ gauge theories quantized on ${\rm AdS}_2 \times S^1$. We compute the index by applying supersymmetric localization to partition functions of vector and chiral multiplets on ${\rm AdS}_2 \times T^2$, with and without a boundary: in both instances we classify normalizability and boundary conditions for gauge, matter and ghost fields. The index is twisted as the dynamical fields are coupled to a R-symmetry background 1-form with non-trivial exterior derivative and proportional to the spin connection. After regularization the index is written in terms of elliptic gamma functions, reminiscent of four-dimensional holomorphic blocks, and crucially depends on the R-charge.

hep-th↗

arXiv2023

The Spindle Index from Localization

We present a new supersymmetric index for three-dimensional ${\cal N}=2$ gauge theories defined on $\Sigma \times S^1$, where $\Sigma$ is a spindle, with twist or anti-twist for the $R$-symmetry background gauge field. We start examining general supersymmetric backgrounds of Euclidean new minimal supergravity admitting two Killing spinors of opposite $R$-charges. We then focus on $\Sigma \times S^1$ and demostrate how to realise twist and anti-twist. We compute the supersymmetric partition functions on such backgrounds via localization and show that these are captured by a general formula, depending on the type of twist, which unifies and generalises the superconformal and topologically twisted indices.

hep-th↗

arXiv2020

Topological Correlators and Surface Defects from Equivariant Cohomology

We find a one-dimensional protected subsector of $\mathcal{N}=4$ matter theories on a general class of three-dimensional manifolds. By means of equivariant localization, we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on $S^3$. Then, we apply it to the novel case of $S^2 \times S^1$ and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncommutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general $\mathcal{N}=(2,2)$ surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.

hep-th↗

arXiv2020

Localization of 4d $\mathcal{N}=1$ theories on $\mathbb{D}^2\times \mathbb{T}^2$

We consider 4d $\mathcal{N}=1$ gauge theories with R-symmetry on a hemisphere times a torus. We apply localization techniques to evaluate the exact partition function through a cohomological reformulation of the supersymmetry transformations. Our results represent the natural elliptic lifts of the lower dimensional analogs as well as a field theoretic derivation of the conjectured 4d holomorphic blocks, from which partition functions of compact spaces with diverse topology can be recovered through gluing. We also analyze the different boundary conditions which can naturally be imposed on the chiral multiplets, which turn out to be either Dirichlet or Robin-like. We show that different boundary conditions are related to each other by coupling the bulk to 3d $\mathcal{N}=1$ degrees of freedom on the boundary three-torus, for which we derive explicit 1-loop determinants.

hep-th↗

arXiv2020

Cohomological Localization of $\mathcal N = 2$ Gauge Theories with Matter

We construct a large class of gauge theories with extended supersymmetry on four-dimensional manifolds with a Killing vector field and isolated fixed points. We extend previous results limited to super Yang-Mills theory to general $\mathcal{N}=2$ gauge theories including hypermultiplets. We present a general framework encompassing equivariant Donaldson-Witten theory and Pestun's theory on $S^4$ as two particular cases. This is achieved by expressing fields in cohomological variables, whose features are dictated by supersymmetry and require a generalized notion of self-duality for two-forms and of chirality for spinors. Finally, we implement localization techniques to compute the exact partition function of the cohomological theories we built up and write the explicit result for manifolds with diverse topologies.

hep-th↗

arXiv2020

Supersymmetric localization of refined chiral multiplets on topologically twisted $ H^2 \times S^1$

We derive the partition function of an $\mathcal N=2$ chiral multiplet on topologically twisted $H^2\times S^1$. The chiral multiplet is coupled to a background vector multiplet encoding a real mass deformation. We consider an $ H^2\times S^1$ metric containing two parameters: one is the $S^1$ radius, while the other gives a fugacity $q$ for the angular momentum on $H^2$. The computation is carried out by means of supersymmetric localization, which provides a finite answer written in terms of $q$-Pochammer symbols and multiple Zeta functions. Especially, the partition function of normalizable fields reproduces three-dimensional holomorphic blocks.

hep-th↗

arXiv2019

Integrable Fishnet from $γ$-Deformed $\mathcal{N}=2$ Quivers

We introduce bi-fermion fishnet theories, a class of models describing integrable sectors of four-dimensional gauge theories with non-maximal supersymmetry. Bi-fermion theories are characterized by a single complex scalar field and two Weyl fermions interacting only via chiral Yukawa couplings. The latter generate oriented Feynman diagrams forming hexagonal lattices, whose fishnet structure signals an underlying integrability that we exploit to compute anomalous dimensions of BMN-vacuum operators. Furthermore, we investigate Lunin-Maldacena deformations of $\mathcal{N}=2$ superconformal field theories with deformation parameter $γ$ and prove that bi-fermion models emerge in the limit of large imaginary $γ$ and vanishing 't Hooft coupling $g$, with $g e^{-i γ/2}$ fixed. Finally, we explicitly find non-trivial conformal fixed points and compute the scaling dimensions of operators for any $γ$ and in presence of double-trace deformations.

hep-th↗

arXiv2017

Yangian Symmetry of String Theory on $AdS_3 \times S^3 \times S^3 \times S^1$ with Mixed 3-form Flux

We find the Yangian symmetry underlying the integrability of type IIB superstrings on $AdS_3 \times S^3 \times S^3 \times S^1$ with mixed Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz flux. The abstract commutation relations of the Yangian are formulated via RTT realisation, while its matrix realisation is in an evaluation representation depending on the quantised coefficient of the Wess-Zumino term. The construction naturally encodes a secret symmetry of the worldsheet scattering matrix whose generators map different Yangian levels to each other. We show that in the large effective string tension limit the Yangian becomes a deformation of a unitary loop algebra and we derive its universal classical r-matrix.

hep-th↗

arXiv2016

The S-matrix algebra of the AdS2 X S2 superstring

In this paper we find the Yangian algebra responsible for the integrability of the AdS2 X S2 X T^6 superstring in the planar limit. We demonstrate the symmetry of the corresponding exact S-matrix in the massive sector, including the presence of the secret symmetry. We give two alternative presentations of the Hopf algebra, along with related discussions on the issue of evaluation representations. We study the classical r-matrix, and re-discover the need for a secret symmetry also in this context. Finally, taking the simplifying zero-coupling limit of the S-matrix as a generating R-matrix for the Algebraic Bethe Ansatz, we obtain an effective model of free fermions on a periodic spin-chain. This limit should provide hints to the one-loop anomalous dimension of the mysterious superconformal quantum mechanics dual to the superstring theory in this geometry.

hep-th↗

arXiv2015

T-Duality of Green-Schwarz Superstrings on AdS(d) x S(d) x M(10-2d)

We verify the self-duality of Green-Schwarz supercoset sigma models on AdS$_d \times S^d $ backgrounds (d=2,3,5) under combined bosonic and fermionic T-dualities without gauge fixing kappa symmetry. We also prove this property for superstrings on AdS$_d \times S^d \times S^d$ (d=2,3) described by supercoset sigma models with the isometries governed by the exceptional Lie supergroups $D(2,1;α)$ (d=2) and $D(2,1;α)\times D(2,1;α)$ (d=3), which requires an additional T-dualisation along one of the spheres. Then, by taking into account the contribution of non-supercoset fermionic modes (up to the second order), we provide evidence for the T-self-duality of the complete type IIA and IIB Green-Schwarz superstring theory on AdS$_d\times S^d \times T^{10-2d}$ (d=2,3) backgrounds with Ramond-Ramond fluxes. Finally, applying the Buscher-like rules to T-dualising supergravity fields, we prove the T-self-duality of the whole class of the AdS$_d\times S^d \times M^{10-2d}$ superbackgrounds with Ramond-Ramond fluxes in the context of supergravity.

hep-th↗

arXiv2014

Integrable S-matrices, massive and massless modes and the AdS_2 x S^2 superstring

We derive the exact S-matrix for the scattering of particular representations of the centrally-extended psu(1|1)^2 Lie superalgebra, conjectured to be related to the massive modes of the light-cone gauge string theory on AdS_2 x S^2 x T^6. The S-matrix consists of two copies of a centrally-extended psu(1|1) invariant S-matrix and is in agreement with the tree-level result following from perturbation theory. Although the overall factor is left unfixed, the constraints following from crossing symmetry and unitarity are given. The scattering involves long representations of the symmetry algebra, and the relevant representation theory is studied in detail. We also discuss Yangian symmetry and find it has a standard form for a particular limit of the aforementioned representations. This has a natural interpretation as the massless limit, and we investigate the corresponding limits of the massive S-matrix. Under the assumption that the massless modes of the light-cone gauge string theory transform in these limiting representations, the resulting S-matrices would provide the building blocks for the full S-matrix. Finally, some brief comments are given on the Bethe ansatz.

hep-th↗

arXiv2014

Secret Symmetries of Type IIB Superstring Theory on AdS3 x S3 x M4

We establish features of so-called Yangian secret symmetries for AdS3 type IIB superstring backgrounds thus verifying the persistence of such symmetries to this new instance of the AdS/CFT correspondence. Specifically, we find two a priori different classes of secret symmetry generators. One class of generators, anticipated from the previous literature, is more naturally embedded in the algebra governing the integrable scattering problem. The other class of generators is more elusive, and somewhat closer in its form to its higher-dimensional AdS5 counterpart. All of these symmetries respect left-right crossing. In addition, by considering the interplay between left and right representations, we gain a new perspective on the AdS5 case. We also study the RTT-realisation of the Yangian in AdS3 backgrounds thus establishing a new incarnation of the Beisert-de Leeuw construction.

hep-th↗

arXiv2013

New coherent states and modified heat equations

We clarify the relations between certain new coherent states for loop quantum gravity and the analytically continued heat kernel coherent states, highlighting the underlying general construction, the presence of a modified heat equation as well as the way in which the properties of the heat kernels are automatically inherited by these new states.

gr-qc↗