arXiv subjects

Guido Festuccia

Publications and source records attributed to Guido Festuccia.

At least 19 recordsLinked to original sources

arXiv2025

The Equivariant B model

In this work, we introduce an equivariant deformation of the $B$ model on the sphere with a $U(1)$-action. We present the deformed supersymmetry transformations and corresponding Lagrangians and study observables in the supercharge cohomology. The inclusion of equivariance allows for the introduction of novel, position-dependent observables on the sphere, which have no counterparts in the conventional $B$ model. Two specific cases we explore in detail are position-dependent superpotentials and complex structure deformations. In both instances, the theory exhibits notable differences from the standard $B$ model, revealing intriguing new features.

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arXiv2022

Localizing non-linear ${\cal N}=(2,2)$ sigma model on $S^2$

We present a systematic study of ${\cal N}=(2,2)$ supersymmetric non-linear sigma models on $S^2$ with the target being a Kähler manifold. We discuss their reformulation in terms of cohomological field theory. In the cohomological formulation we use a novel version of 2D self-duality which involves a $U(1)$ action on $S^2$. In addition to the generic model we discuss the theory with target space equivariance corresponding to a supersymmetric sigma model coupled to a non-dynamical supersymmetric background gauge multiplet. We discuss the localization locus and perform a one-loop calculation around the constant maps. We argue that the theory can be reduced to some exotic model over the moduli space of holomorphic disks.

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arXiv2020

Consistency of supersymmetric 't Hooft anomalies

We consider recent claims that supersymmetry is anomalous in the presence of a R-symmetry anomaly. We revisit arguments that such an anomaly in supersymmetry can be removed and write down an explicit counterterm that accomplishes it. Removal of the supersymmetry anomaly requires enlarging the corresponding current multiplet. As a consequence the Ward identities for other symmetries that are already anomalous acquire extra terms. This procedure can only be impeded when the choice of current multiplet is forced. We show how Wess-Zumino consistency conditions are modified when the anomaly is removed. Finally we check that the modified Wess-Zumino consistency conditions are satisfied, and supersymmetry unbroken, in an explicit one loop computation using Pauli-Villars regulators. To this end we comment on how to use Pauli-Villars to regulate correlators of components of (super)current multiplets in a manifestly supersymmetric way.

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arXiv2020

S-duality and supersymmetry on curved manifolds

We perform a systematic study of S-duality for ${\cal N}=2$ supersymmetric non-linear abelian theories on a curved manifold. Localization can be used to compute certain supersymmetric observables in these theories. We point out that localization and S-duality acting as a Legendre transform are not compatible. For these theories S-duality should be interpreted as Fourier transform and we provide some evidence for this. We also suggest the notion of a coholomological prepotential for an abelian theory that gives the same partition function as a given non-abelian supersymmetric theory.

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arXiv2020

Transversally Elliptic Complex and Cohomological Field Theory

This work is a continuation of our previous paper arXiv:1812.06473 where we have constructed ${\cal N}=2$ supersymmetric Yang-Mills theory on 4D manifolds with a Killing vector field with isolated fixed points. In this work we expand on the mathematical aspects of the theory, with a particular focus on its nature as a cohomological field theory. The well-known Donaldson-Witten theory is a twisted version of ${\cal N}=2$ SYM and can also be constructed using the Atiyah-Jeffrey construction. This theory is concerned with the moduli space of anti-self-dual gauge connections, with a deformation theory controlled by an elliptic complex. More generally, supersymmetry requires considering configurations that look like either instantons or anti-instantons around fixed points, which we call flipping instantons. The flipping instantons of our 4D ${\cal N}=2$ theory are derived from the 5D contact instantons. The novelty is that their deformation theory is controlled by a transversally elliptic complex, which we demonstrate here. We repeat the Atiyah-Jeffrey construction in the equivariant setting and arrive at the Lagrangian (an equivariant Euler class in the relevant field space) that was also obtained from our previous work arXiv:1812.06473. We show that the transversal ellipticity of the deformation complex is crucial for the non-degeneracy of the Lagrangian and the calculability of the theory. Our construction is valid on a large class of quasi toric 4 manifolds.

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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.

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arXiv2020

Twisting with a Flip (the Art of Pestunization)

We construct ${\cal N}=2$ supersymmetric Yang-Mills theory on 4D manifolds with a Killing vector field with isolated fixed points. It turns out that for every fixed point one can allocate either instanton or anti-instanton contributions to the partition function, and that this is compatible with supersymmetry. The equivariant Donaldson-Witten theory is a special case of our construction. We present a unified treatment of Pestun's calculation on $S^4$ and equivariant Donaldson-Witten theory by generalizing the notion of self-duality on manifolds with a vector field. We conjecture the full partition function for a ${\cal N}=2$ theory on any 4D manifold with a Killing vector. Using this new notion of self-duality to localize a supersymmetric theory is what we call "Pestunization".

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arXiv2019

Metastable Vacua in Large-$N$ QCD$_3$

We reexamine the vacuum structure of three-dimensional quantum chromodynamics (QCD$_3$) with gauge group $SU(N)$, $N_f$ fundamental quark flavors, and a level-$k$ Chern-Simons term. This analysis can be reliably carried out in the large-$N$, fixed $N_f, k$ limit of the theory, up to certain assumptions that we spell out explicitly. At leading order in the large-$N$ expansion we find $N_f + 1$ distinct, exactly degenerate vacuum superselection sectors with different patterns of flavor-symmetry breaking. The associated massless Nambu-Goldstone bosons are generically accompanied by topological Chern-Simons theories. This set of vacua contains many candidate phases previously proposed for QCD$_3$. At subleading order in the large-$N$ expansion, the exact degeneracy between the different superselection sectors is lifted, leading to a multitude of metastable vacua. If we dial the quark masses, different metastable vacua can become the true vacuum of the theory, leading to a sequence of first-order phase transitions. This intricate large-$N$ dynamics can be captured by the previously proposed bosonic dual theories for QCD$_3$, provided these bosonic duals are furnished with a suitable scalar potential. Interestingly, this potential must include terms beyond quartic order in the scalar fields.

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arXiv2018

General Relativity from Scattering Amplitudes

We outline the program to apply modern quantum field theory methods to calculate observables in classical general relativity through a truncation to classical terms of the multi-graviton two-body on-shell scattering amplitudes between massive fields. Since only long-distance interactions corresponding to non-analytic pieces need to be included, unitarity cuts provide substantial simplifications for both post-Newtonian and post-Minkowskian expansions. We illustrate this quantum field theoretic approach to classical general relativity by computing the interaction potentials to second order in the post-Newtonian expansion, as well as the scattering functions for two massive objects to second order in the post-Minkowskian expansion. We also derive an all-order exact result for gravitational light-by-light scattering.

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arXiv2017

N=2 supersymmetric gauge theory on connected sums of $S^2\times S^2$

We construct 4D $\mathcal{N}=2$ theories on an infinite family of 4D toric manifolds with the topology of connected sums of $S^2 \times S^2$. These theories are constructed through the dimensional reduction along a non-trivial $U(1)$-fiber of 5D theories on toric Sasaki-Einstein manifolds. We discuss the conditions under which such reductions can be carried out and give a partial classification result of the resulting 4D manifolds. We calculate the partition functions of these 4D theories and they involve both instanton and anti-instanton contributions, thus generalizing Pestun's famous result on $S^4$.

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arXiv2016

Symmetries and Couplings of Non-Relativistic Electrodynamics

We examine three versions of non-relativistic electrodynamics, known as the electric and magnetic limit theories of Maxwell's equations and Galilean electrodynamics (GED) which is the off-shell non-relativistic limit of Maxwell plus a free scalar field. For each of these three cases we study the couplings to non-relativistic dynamical charged matter (point particles and charged complex scalars). The GED theory contains besides the electric and magnetic potentials a so-called mass potential making the mass parameter a local function. The electric and magnetic limit theories can be coupled to twistless torsional Newton-Cartan geometry while GED can be coupled to an arbitrary torsional Newton-Cartan background. The global symmetries of the electric and magnetic limit theories on flat space consist in any dimension of the infinite dimensional Galilean conformal algebra and a $U(1)$ current algebra. For the on-shell GED theory this symmetry is reduced but still infinite dimensional, while off-shell only the Galilei algebra plus two dilatations remain. Hence one can scale time and space independently, allowing Lifshitz scale symmetries for any value of the critical exponent $z$.

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arXiv2016

Torsional Newton-Cartan Geometry from the Noether Procedure

We apply the Noether procedure for gauging space-time symmetries to theories with Galilean symmetries, analyzing both massless and massive (Bargmann) realizations. It is shown that at the linearized level the Noether procedure gives rise to (linearized) torsional Newton-Cartan geometry. In the case of Bargmann theories the Newton-Cartan form $M_μ$ couples to the conserved mass current. We show that even in the case of theories with massless Galilean symmetries it is necessary to introduce the form $M_μ$ and that it couples to a topological current. Further, we show that the Noether procedure naturally gives rise to a distinguished affine (Christoffel type) connection that is linear in $M_μ$ and torsionful. As an application of these techniques we study the coupling of Galilean electrodynamics to TNC geometry at the linearized level.

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arXiv2015

Instanton Effects in Three Flavor QCD

Recently it was shown that in QCD-like theories with $N_f > N$, where $N_f$ is the number of light flavors and $N$ is the number of colors, there are correlation functions that vanish in perturbation theory and at short distances receive dominant, calculable contributions from small instantons. Here we extend the set of such objects to theories with $N_f = N$, which includes real QCD, and discuss their application as a calibration of lattice computations at small quark mass. We revisit the related issue of the $u$ quark mass and its additive renormalization by small instantons, and discuss an alternative test of $m_u=0$ on the lattice.

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arXiv2015

Dynamical generation of the Peccei-Quinn scale in gauge mediation

The Peccei-Quinn (PQ) mechanism provides an elegant solution to the strong CP problem. However astrophysical constraints on axions require the PQ breaking scale to be far higher than the electroweak scale. In supersymmetric models the PQ symmetry can be broken at an acceptable scale if the effective potential for the pseudo-modulus in the axion multiplet develops a minimum at large enough field values. In this work we classify systematically hadronic axion models in the context of gauge mediation and study their effective potentials at one loop. We find that some models generate a PQ scale comparable to the messenger scale. Our result may prove useful for constructing full realistic models of gauge mediation that address the strong CP problem. We also comment briefly on the cosmological aspects related to saxion and axino, and on the quality of the PQ symmetry.

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arXiv2014

From Rigid Supersymmetry to Twisted Holomorphic Theories

We study N=1 field theories with a U(1)_R symmetry on compact four-manifolds M. Supersymmetry requires M to be a complex manifold. The supersymmetric theory on M can be described in terms of conventional fields coupled to background supergravity, or in terms of twisted fields adapted to the complex geometry of M. Many properties of the theory that are difficult to see in one formulation are simpler in the other one. We use the twisted description to study the dependence of the partition function Z_M on the geometry of M, as well as coupling constants and background gauge fields, recovering and extending previous results. We also indicate how to generalize our analysis to three-dimensional N=2 theories with a U(1)_R symmetry. In this case supersymmetry requires M to carry a transversely holomorphic foliation, which endows it with a near-perfect analogue of complex geometry. Finally, we present new explicit formulas for the dependence of Z_M on the choice of U(1)_R symmetry in four and three dimensions, and illustrate them for complex manifolds diffeomorphic to S^3 x S^1, as well as general squashed three-spheres.

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arXiv2013

The Geometry of Supersymmetric Partition Functions

We consider supersymmetric field theories on compact manifolds M and obtain constraints on the parameter dependence of their partition functions Z_M. Our primary focus is the dependence of Z_M on the geometry of M, as well as background gauge fields that couple to continuous flavor symmetries. For N=1 theories with a U(1)_R symmetry in four dimensions, M must be a complex manifold with a Hermitian metric. We find that Z_M is independent of the metric and depends holomorphically on the complex structure moduli. Background gauge fields define holomorphic vector bundles over M and Z_M is a holomorphic function of the corresponding bundle moduli. We also carry out a parallel analysis for three-dimensional N=2 theories with a U(1)_R symmetry, where the necessary geometric structure on M is a transversely holomorphic foliation (THF) with a transversely Hermitian metric. Again, we find that Z_M is independent of the metric and depends holomorphically on the moduli of the THF. We discuss several applications, including manifolds diffeomorphic to S^3 x S^1 or S^2 x S^1, which are related to supersymmetric indices, and manifolds diffeomorphic to S^3 (squashed spheres). In examples where Z_M has been calculated explicitly, our results explain many of its observed properties.

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arXiv2013

Supersymmetric Field Theories on Three-Manifolds

We construct supersymmetric field theories on Riemannian three-manifolds M, focusing on N=2 theories with a U(1)_R symmetry. Our approach is based on the rigid limit of new minimal supergravity in three dimensions, which couples to the flat-space supermultiplet containing the R-current and the energy-momentum tensor. The field theory on M possesses a single supercharge, if and only if M admits an almost contact metric structure that satisfies a certain integrability condition. This may lead to global restrictions on M, even though we can always construct one supercharge on any given patch. We also analyze the conditions for the presence of additional supercharges. In particular, two supercharges of opposite R-charge exist on every Seifert manifold. We present general supersymmetric Lagrangians on M and discuss their flat-space limit, which can be analyzed using the R-current supermultiplet. As an application, we show how the flat-space two-point function of the energy-momentum tensor in N=2 superconformal theories can be calculated using localization on a squashed sphere.

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arXiv2012

Comments on Chern-Simons Contact Terms in Three Dimensions

We study contact terms of conserved currents and the energy-momentum tensor in three-dimensional quantum field theory. They are associated with Chern-Simons terms for background fields. While the integer parts of these contact terms are ambiguous, their fractional parts are meaningful physical observables. In N=2 supersymmetric theories with a U(1)_R symmetry some of these observables lead to an anomaly. Moreover, they can be computed exactly using localization, leading to new tests of dualities.

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