arXiv subjects

Stefano Cremonesi

Publications and source records attributed to Stefano Cremonesi.

At least 19 recordsLinked to original sources

arXiv2024

Zig-zag deformations of toric quiver gauge theories. Part I: reflexive polytopes

We study one-parameter families of $U(1)^2$ preserving deformations relating pairs of toric quiver gauge theories on D-branes probing local toric (pseudo) del Pezzo surfaces. The superpotential deformations are defined by zig-zag paths in the brane tiling and are non-trivial in the chiral ring if the geometry has a non-isolated singularity. In the dual $(p,q)$ web, the deformation is realized as a Hanany-Witten move that reverses a semi-infinite fivebrane. We use these deformations to find RG flows between 4d $\mathcal{N}=1$ SCFTs on D3-branes probing local toric (pseudo) del Pezzo surfaces of the same degree, and briefly comment on the interpretation for BPS quivers of rank one 5d SCFTs on $S^1$.

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arXiv2022

Semiclassics of three-dimensional SCFTs from holography

We use holography to compute the large-$N$ effective field theory along the moduli space of vacua of an infinite class of three-dimensional $\mathcal{N}=2$ SCFTs admitting a dual M-theory description. We focus in particular on toric models and show how the spectrum of large $R$-charge SCFT chiral scalar operators corresponds to a set of explicit semiclassical solutions of our effective field theory, which describe bound states of backreacting giant gravitons and baryonic-like M5-branes. Our semiclassical description allows for a direct computation of the scaling dimensions of these operators and provides a starting point for a semiclassical investigation of the SCFT data in the large $R$-charge sector. We consider the models corresponding to the $Y^{12}(\mathbb{P}^2)$ and $Q^{111}$ Sasaki-Einstein spaces as explicit examples.

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arXiv2020

Quantized Coulomb Branches, Monopole Bubbling and Wall-Crossing Phenomena in 3d $\mathcal{N}=4$ Theories

To study the quantized Coulomb branch of 3d $\mathcal{N}=4$ unitary SQCD theories, we propose a new method to compute correlators of monopole and Casimir operators that are inserted in the $\mathbb{R}\times\mathbb{R}^2_ε$ Omega background. This method combines results from supersymmetric localization with inputs from the brane realisation of the correlators in type IIB string theory. The main challenge is the computation of the partition functions of certain Super-Matrix-Models (SMMs), which appear in the contribution of monopole bubbling sectors and are realised as the theory living on the D1 strings in the brane construction. We find that the non-commutativity arising in the monopole operator insertions is related to a wall-crossing phenomenon in the FI parameter space of the SMM. We illustrate our method in various examples and we provide explicit results for arbitrary correlators of non-bubbling bare monopole operators. We also discuss the realisation of the non-commutative product as a Moyal (star) product and use it to successfully test our results.

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arXiv2018

The Infrared Fixed Points of 3d $\mathcal{N}=4$ $USp(2N)$ SQCD Theories

We derive the algebraic description of the Coulomb branch of 3d $\mathcal{N}=4$ $USp(2N)$ SQCD theories with $N_f$ fundamental hypermultiplets and determine their low energy physics in any vacuum from the local geometry of the moduli space, identifying the interacting SCFTs which arise at singularities and possible extra free sectors. The SCFT with the largest moduli space arises at the most singular locus on the Coulomb branch. For $N_f>2N$ (good theories) it sits at the origin of the conical variety as expected. For $N_f =2N$ we find two separate most singular points, from which the two isomorphic components of the Higgs branch of the UV theory emanate. The SCFTs sitting at any of these two vacua have only odd dimensional Coulomb branch generators, which transform under an accidental $SU(2)$ global symmetry. We provide a direct derivation of their moduli spaces of vacua, and propose a Lagrangian mirror theory for these fixed points. For $2 \le N_f < 2N$ the most singular locus has one or two extended components, for $N_f$ odd or even, and the low energy theory involves an interacting SCFT of one of the above types, plus free twisted hypermultiplets. For $N_f=0,1$ the Coulomb branch is smooth. We complete our analysis by studying the low energy theory at the symmetric vacuum of theories with $N < N_f \le 2N$, which exhibits a local Seiberg-like duality.

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arXiv2018

The Infrared Physics of Bad Theories

We study the complete moduli space of vacua of 3d $\mathcal{N}=4$ $U(N)$ SQCD theories with $N_f$ fundamentals, building on the algebraic description of the Coulomb branch, and deduce the low energy physics in any vacuum from the local geometry of the moduli space. We confirm previous claims for good and ugly SQCD theories, and show that bad theories flow to the same interacting fixed points as good theories with additional free twisted hypermultiplets. A Seiberg-like duality proposed for bad theories with $N \le N_f \le 2N-2$ is ruled out: the spaces of vacua of the putative dual theories are different. However such bad theories have a distinguished vacuum, which preserves all the global symmetries, whose infrared physics is that of the proposed dual. We finally explain previous results on sphere partition functions and elucidate the relation between the UV and IR $R$-symmetry in this symmetric vacuum.

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arXiv2017

3d supersymmetric gauge theories and Hilbert series

The Hilbert series is a generating function that enumerates gauge invariant chiral operators of a supersymmetric field theory with four supercharges and an R-symmetry. In this article I review how counting dressed 't Hooft monopole operators leads to a formula for the Hilbert series of a 3d $\mathcal{N}\geq 2$ gauge theory, which captures precious information about the chiral ring and the moduli space of supersymmetric vacua of the theory.

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arXiv2017

Instanton Operators and the Higgs Branch at Infinite Coupling

The richness of 5d $\mathcal{N}=1$ theories with a UV fixed point at infinite coupling is due to the existence of local disorder operators known as instanton operators. By considering the Higgs branch of $SU(2)$ gauge theories with $N_f \leq 7$ flavours at finite and infinite coupling, we write down the explicit chiral ring relations between instanton operators, the glueball superfield and mesons. Exciting phenomena appear at infinite coupling: the glueball superfield is no longer nilpotent and the classical chiral ring relations are quantum corrected by instanton operators bilinears. We also find expressions for the dressing of instanton operators of arbitrary charge. The same analysis is performed for $USp(2k)$ with an antisymmetric hypermultiplet and pure $SU(N)$ gauge theories.

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arXiv2016

6d holographic anomaly match as a continuum limit

An infinite class of analytic AdS_7 x S^3 solutions has recently been found. The S^3 is distorted into a "crescent roll" shape by the presence of D8-branes. These solutions are conjectured to be dual to a class of "linear quivers", with a large number of gauge groups coupled to (bi-)fundamental matter and tensor fields. In this paper we perform a precise quantitative check of this correspondence, showing that the a Weyl anomalies computed in field theory and gravity agree. In the holographic limit, where the number of gauge groups is large, the field theory result is a quadratic form in the gauge group ranks involving the inverse of the A_N Cartan matrix C. The agreement can be understood as a continuum limit, using the fact that C is a lattice analogue of a second derivative. The discrete data of the field theory, summarized by two partitions, become in this limit the continuous functions in the geometry. Conversely, the geometry of the internal space gets discretized at the quantum level to the discrete data of the two partitions.

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arXiv2016

The moduli spaces of $3d$ ${\cal N} \ge 2$ Chern-Simons gauge theories and their Hilbert series

We present a formula for the Hilbert series that counts gauge invariant chiral operators in a large class of 3d ${\cal N} \ge 2$ Yang-Mills-Chern-Simons theories. The formula counts 't Hooft monopole operators dressed by gauge invariants of a residual gauge theory of massless fields in the monopole background. We provide a general formula for the case of abelian theories, where nonperturbative corrections are absent, and consider a few examples of nonabelian theories where nonperturbative corrections are well understood. We also analyze in detail nonabelian ABJ(M) theories as well as worldvolume theories of M2-branes probing Calabi-Yau fourfold and hyperKähler twofold singularities with ${\cal N} = 2$ and ${\cal N} = 3$ supersymmetry.

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arXiv2015

The equivariant A-twist and gauged linear sigma models on the two-sphere

We study two-dimensional $\mathcal{N}=(2,2)$ supersymmetric gauged linear sigma models (GLSM) on the $Ω$-deformed sphere, $S^2_Ω$, which is a one-parameter deformation of the $A$-twisted sphere. We provide an exact formula for the $S^2_Ω$ supersymmetric correlation functions using supersymmetric localization. The contribution of each instanton sector is given in terms of a Jeffrey-Kirwan residue on the Coulomb branch. In the limit of vanishing $Ω$-deformation, the localization formula greatly simplifies the computation of $A$-twisted correlation functions, and leads to new results for non-abelian theories. We discuss a number of examples and comment on the $ε_Ω$-deformation of the quantum cohomology relations. Finally, we present a complementary Higgs branch localization scheme in the special case of abelian gauge groups.

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arXiv2015

The Hilbert series of 3d N=2 Yang-Mills theories with vectorlike matter

This paper presents a formula for the Hilbert series that counts gauge invariant chiral operators in 3d N=2 Yang-Mills theories with vectorlike matter and no Chern-Simons interactions. The formula counts 't Hooft monopole operators dressed by gauge invariants of a residual gauge theory of massless fields in the monopole background, which is determined by the Higgs mechanism. The sum over magnetic charges is restricted due to instanton effects that partially lift the classical Coulomb branch. The formalism is applied to unitary and symplectic gauge theories with fundamental matter, reproducing old results for the moduli space of vacua and the chiral ring, without resorting to any further effective superpotential on the moduli space.

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arXiv2014

T^σ_ρ(G) Theories and Their Hilbert Series

We give an explicit formula for the Higgs and Coulomb branch Hilbert series for the class of 3d N=4 superconformal gauge theories T^σ_ρ(G) corresponding to a set of D3 branes ending on NS5 and D5-branes, with or without O3 planes. Here G is a classical group, σis a partition of G and ρa partition of the dual group G^\vee. In deriving such a formula we make use of the recently discovered formula for the Hilbert series of the quantum Coulomb branch of N=4 superconformal theories. The result can be expressed in terms of a generalization of a class of symmetric functions, the Hall-Littlewood polynomials, and can be interpreted in mathematical language in terms of localization. We mainly consider the case G=SU(N) but some interesting results are also given for orthogonal and symplectic groups.

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arXiv2014

Coulomb Branch and The Moduli Space of Instantons

The moduli space of instantons on C^2 for any simple gauge group is studied using the Coulomb branch of N=4 gauge theories in three dimensions. For a given simple group G, the Hilbert series of such an instanton moduli space is computed from the Coulomb branch of the quiver given by the over-extended Dynkin diagram of G. The computation includes the cases of non-simply-laced gauge groups G, complementing the ADHM constructions which are not available for exceptional gauge groups. Even though the Lagrangian description for non-simply laced Dynkin diagrams is not currently known, the prescription for computing the Coulomb branch Hilbert series of such diagrams is very simple. For instanton numbers one and two, the results are in agreement with previous works. New results and general features for the moduli spaces of three and higher instanton numbers are reported and discussed in detail.

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arXiv2014

Coulomb branch Hilbert series and Hall-Littlewood polynomials

There has been a recent progress in understanding the chiral ring of 3d $\mathcal{N}=4$ superconformal gauge theories by explicitly constructing an exact generating function (Hilbert series) counting BPS operators on the Coulomb branch. In this paper we introduce Coulomb branch Hilbert series in the presence of background magnetic charges for flavor symmetries, which are useful for computing the Hilbert series of more general theories through gluing techniques. We find a simple formula of the Hilbert series with background magnetic charges for $T_ρ(G)$ theories in terms of Hall-Littlewood polynomials. Here $G$ is a classical group and $ρ$ is a certain partition related to the dual group of $G$. The Hilbert series for vanishing background magnetic charges show that Coulomb branches of $T_ρ(G)$ theories are complete intersections. We also demonstrate that mirror symmetry maps background magnetic charges to baryonic charges.

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arXiv2014

Coulomb branch Hilbert series and Three Dimensional Sicilian Theories

We evaluate the Coulomb branch Hilbert series of mirrors of three dimensional Sicilian theories, which arise from compactifying the $6d$ $(2,0)$ theory with symmetry $G$ on a circle times a Riemann surface with punctures. We obtain our result by gluing together the Hilbert series for building blocks $T_{\mathbfρ}(G)$, where $\mathbfρ$ is a certain partition related to the dual group of $G$, which we evaluated in a previous paper. The result is expressed in terms of a class of symmetric functions, the Hall-Littlewood polynomials. As expected from mirror symmetry, our results agree at genus zero with the superconformal index prediction for the Higgs branch Hilbert series of the Sicilian theories and extend it to higher genus. In the $A_1$ case at genus zero, we also evaluate the Coulomb branch Hilbert series of the Sicilian theory itself, showing that it only depends on the number of external legs.

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arXiv2014

Partition functions of N=(2,2) gauge theories on S^2 and vortices

We apply localization techniques to compute the partition function of a two-dimensional N=(2,2) R-symmetric theory of vector and chiral multiplets on S^2. The path integral reduces to a sum over topological sectors of a matrix integral over the Cartan subalgebra of the gauge group. For gauge theories which would be completely Higgsed in the presence of a Fayet-Iliopoulos term in flat space, the path integral alternatively reduces to the product of a vortex times an antivortex partition functions, weighted by semiclassical factors and summed over isolated points on the Higgs branch. As applications we evaluate the partition function for some U(N) gauge theories, showing equality of the path integrals for theories conjectured to be dual by Hori and Tong and deriving new expressions for vortex partition functions.

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arXiv2014

Mass-deformed Brane Tilings

We study renormalization group flows among N=1 SCFTs realized on the worldvolume of D3-branes probing toric Calabi-Yau singularities, thus admitting a brane tiling description. The flows are triggered by masses for adjoint or vector-like pairs of bifundamentals and are generalizations of the Klebanov-Witten construction of the N=1 theory for the conifold starting from the N=2 theory for the C^2/Z_2 orbifold. In order to preserve the toric condition pairs of masses with opposite signs have to be switched on. We offer a geometric interpretation of the flows as complex deformations of the Calabi-Yau singularity preserving the toric condition. For orbifolds, we support this interpretation by an explicit string amplitude computation of the gauge invariant mass terms generated by imaginary self-dual 3-form fluxes in the twisted sector. In agreement with the holographic a-theorem, the volume of the Sasaki-Einstein 5-base of the Calabi-Yau cone always increases along the flow.

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arXiv2014

Comments on N=(2,2) Supersymmetry on Two-Manifolds

We study curved-space rigid supersymmetry for two-dimensional $\mathcal{N}=(2,2)$ supersymmetric fields theories with a vector-like $R$-symmetry by coupling such theories to background supergravity. The associated Killing spinors can be viewed as holomorphic sections of particular complex line bundles over Euclidean space-time, which severely restrict the allowed supersymmetric couplings on compact orientable Riemann surfaces without boundaries. For genus $g>1$, the only consistent non-singular couplings are the ones dictated by the topological $A$-twist. On spaces with $S^2$ topology, there exist additional supersymmetric backgrounds with $m=0$ or $\pm 1$ unit of flux for the $R$-symmetry gauge field. The $m=-1$ case includes the $Ω$-background on the sphere. We also systematically work out the curved-space supersymmetry multiplets and supersymmetric Lagrangians.

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