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Diego Rodriguez-Gomez

Publications and source records attributed to Diego Rodriguez-Gomez.

At least 37 records · Page 2Linked to original sources
arXiv2022

Quivers, Lattice Gauge Theories and Fractons

We argue that quiver gauge theories with $SU(N)$ gauge groups give rise to lattice gauge theories with matter possessing fractonic properties, where the lattice is the quiver itself. This idea extends a recent proposal by Razamat. This class of theories exhibit a $\mathbb{Z}_N$ 1-form global symmetry that can be used to classify their phases. The order parameter of this transition is the expectation value of Wilson loops, which correspond to mesonic operators in the underlying quiver gauge theory. We discuss how this perspective naturally fits with the deconstruction of a higher dimensional theory.

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arXiv2020

The Cat's Cradle: Deforming the higher rank $E_1$ and $\tilde{E}_1$ theories

We use 5-brane webs to study the two-dimensional space of supersymmetric mass deformations of higher rank generalizations of the 5d $E_1$ and $\tilde{E}_1$ theories. Some of the resulting IR phases are described by IR free supersymmetric gauge theories, while others correspond to interacting fixed points. The number of different phases appears to grow with the rank. The space of deformations is qualitatively different for the even and odd rank cases, but that of the even (odd) rank $E_1$ theory is similar to that of the odd (even) rank $\tilde{E}_1$ theory. One result of our analysis predicts that the supersymmetric $SU(N)$ theory with CS level $k=\frac{N}{2} + 4$ and a single massless antisymmetric hypermultiplet exhibits an enhanced global symmetry at the UV fixed point, given by $SU(2)\times SU(2)$ if $N$ is even, and $SU(2)\times U(1)$ if $N$ is odd.

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arXiv2020

On the UV completion of the $O(N)$ model in $6-ε$ dimensions: a stable large-charge sector

We study large charge sectors in the $O(N)$ model in $6-ε$ dimensions. For $4<d<6$, in perturbation theory, the quartic $O(N)$ theory has a UV stable fixed point at large $N$. It was recently argued that this fixed point can be described in terms of an IR fixed point of a cubic $O(N)$ model. By considering a double scaling limit of large charge and weak couplings, we compute two-point and all "extremal" higher-point correlation functions for large charge operators and find a precise equivalence between both pictures. Instanton instabilities are found to be exponentially suppressed at large charge. We also consider correlation function of $U(1)$-invariant meson operators in the $O(2N)\supset U(1)\times SU(N)$ theory, as a first step towards tests of (higher spin) $AdS/CFT$.

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arXiv2020

Discrete gauge theories of charge conjugation

We define gauge theories whose gauge group includes charge conjugation as well as standard $\mathrm{SU}(N)$ transformations. When combined, these transformations form a novel type of group with a semidirect product structure. For $N$ even, we show that there are exactly two possible such groups which we dub $\widetilde{\mathrm{SU}}(N)_{\mathrm{I,II}}$. We construct the transformation rules for the fundamental and adjoint representations, allowing us to explicitly build four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories based on $\widetilde{\mathrm{SU}}(N)_{\mathrm{I,II}}$ and understand from first principles their global symmetry. We compute the Haar measure on the groups, which allows us to quantitatively study the operator content in protected sectors by means of the superconformal index. In particular, we find that both types of $\widetilde{\mathrm{SU}}(N)_{\mathrm{I,II}}$ groups lead to non-freely generated Coulomb branches.

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arXiv2020

Correlation functions in scalar field theory at large charge

We compute general higher-point functions in the sector of large charge operators $ϕ^n$, $\barϕ^n$ at large charge in $O(2)$ $(\bar ϕϕ)^2$ theory. We find that there is a special class of "extremal" correlators having only one insertion of $\bar ϕ^n$ that have a remarkably simple form in the double-scaling limit $n\to \infty $ at fixed $g\,n^2\equiv λ$, where $g\simε$ is the coupling at the $O(2)$ Wilson-Fisher fixed point in $4-ε$ dimensions. In this limit, also non-extremal correlators can be computed. As an example, we give the complete formula for $ \langle ϕ(x_1)^{n}\,ϕ(x_2)^{n}\,\barϕ(x_3)^{n}\,\barϕ(x_4)^{n}\rangle$, which reveals an interesting structure.

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arXiv2019

Free energy and boundary anomalies on $\mathbb{S}^a\times \mathbb{H}^b$ spaces

We compute free energies as well as conformal anomalies associated with boundaries for a conformal free scalar field. To that matter, we introduce the family of spaces of the form $\mathbb{S}^a\times \mathbb{H}^b$, which are conformally related to $\mathbb{S}^{a+b}$. For the case of $a=1$, related to the entanglement entropy across $\mathbb{S}^{b-1}$, we provide some new explicit computations of entanglement entropies at weak coupling. We then compute the free energy for spaces $\mathbb{S}^a\times \mathbb{H}^b$ for different values of $a$ and $b$. For spaces $\mathbb{S}^{2n+1}\times \mathbb{H}^{2k}$ we find an exact match with the free energy on $\mathbb{S}^{2n+2k+1}$. For $\mathbb{H}^{2k+1}$ and $\mathbb{S}^{3}\times \mathbb{H}^{3}$ we find conformal anomalies originating from boundary terms. We also compute the free energy for strongly coupled theories through holography, obtaining similar results.

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arXiv2019

Supersymmetric probes in warped $AdS_6$

We consider defects in 5d field theories corresponding to higher-rank generalizations of the $E_{N_f+1}$ theories; holographically dual to the Brandhuber-Oz background in type I' String Theory. We concentrate on codimension 2 and 1 defects, corresponding, respectively, to 3d and 4d defect Quantum Field Theories. We study holographically such defect theories by considering supersymmetric probe D4- and D6-branes in the $AdS_6$, whose fluctuations allow us to study the spectrum of mesonic operators of the defect theories. In the case of D4-branes, we also consider wrappings in the internal space which can be regarded as generalizations of the configurations capturing the antisymmetric Wilson loop.

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arXiv2019

Gauge theories from principally extended disconnected gauge groups

We introduce gauge theories based on a class of disconnected gauge groups, called principal extensions. Although in this work we focus on 4d theories with N=2 SUSY, such construction is independent of spacetime dimensions and supersymmetry. These groups implement in a consistent way the discrete gauging of charge conjugation, for arbitrary rank. Focusing on the principal extension of SU(N), we explain how many of the exact methods for theories with 8 supercharges can be put into practice in that context. We then explore the physical consequences of having a disconnected gauge group: we find that the Coulomb branch is generically non-freely generated, and the global symmetry of the Higgs branch is modified in a non-trivial way.

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arXiv2018

Universality of Toda equation in ${\cal N}=2$ superconformal field theories

We show that extremal correlators in all Lagrangian ${\cal N}=2$ superconformal field theories with a simple gauge group are governed by the same universal Toda system of equations, which dictates the structure of extremal correlators to all orders in the perturbation series. A key point is the construction of a convenient orthogonal basis for the chiral ring, by arranging towers of operators in order of increasing dimension, which has the property that the associated two-point functions satisfy decoupled Toda chain equations. We explicitly verify this in all known SCFTs based on $\mathrm{SU}(N)$ gauge groups as well as in superconformal QCD based on orthogonal and symplectic groups. As a by-product, we find a surprising non-renormalization property for the ${\cal N}=2$ $\mathrm{SU}(N)$ SCFT with one hypermultiplet in the rank-2 symmetric representation and one hypermultiplet in the rank-2 antisymmetric representation, where the two-loop terms of a large class of supersymmetric observables identically vanish.

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arXiv2018

Testing $AdS_6/CFT_5$ in Type IIB with stringy operators

We provide further evidence that the recently constructed warped $AdS_6$ solutions in Type IIB supergravity are dual to 5d SCFTs that correspond to $(p,q)$ 5-brane webs with large numbers of like-charged external 5-branes. We study a number of specific examples, including the $T_N$ theory, and identify the bulk states dual to a class of operators with ${\cal O}(N)$ scaling dimensions in terms of strings and string-webs embedded in the solutions.

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arXiv2018

A limit for large $R$-charge correlators in $\mathcal{N}=2$ theories

Using supersymmetric localization, we study the sector of chiral primary operators $({\rm Tr} \, ϕ^2 )^n$ with large $R$-charge $4n$ in $\mathcal{N}=2$ four-dimensional superconformal theories in the weak coupling regime $g\rightarrow 0$, where $λ\equiv g^2n$ is kept fixed as $n\to\infty $, $g$ representing the gauge theory coupling(s). In this limit, correlation functions $G_{2n}$ of these operators behave in a simple way, with an asymptotic behavior of the form $G_{2n}\approx F_{\infty}(λ) \left(\fracλ{2πe}\right)^{2n}\ n^α$, modulo $O(1/n)$ corrections, with $α=\frac{1}{2} \mathrm{dim}(\mathfrak{g})$ for a gauge algebra $\mathfrak{g}$ and a universal function $F_{\infty}(λ)$. As a by-product we find several new formulas both for the partition function as well as for perturbative correlators in ${\cal N}=2$ $\mathfrak{su}(N)$ gauge theory with $2N$ fundamental hypermultiplets.

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arXiv2017

Boundary Conformal Anomalies on Hyperbolic Spaces and Euclidean Balls

We compute conformal anomalies for conformal field theories with free conformal scalars and massless spin $1/2$ fields in hyperbolic space $\mathbb{H}^d$ and in the ball $\mathbb{B}^d$, for $2\leq d\leq 7$. These spaces are related by a conformal transformation. In even dimensional spaces, the conformal anomalies on $\mathbb{H}^{2n}$ and $\mathbb{B}^{2n}$ are shown to be identical. In odd dimensional spaces, the conformal anomaly on $\mathbb{B}^{2n+1}$ comes from a boundary contribution, which exactly coincides with that of $\mathbb{H}^{2n+1}$ provided one identifies the UV short-distance cutoff on $\mathbb{B}^{2n+1}$ with the inverse large distance IR cutoff on $\mathbb{H}^{2n+1}$, just as prescribed by the conformal map. As an application, we determine, for the first time, the conformal anomaly coefficients multiplying the Euler characteristic of the boundary for scalars and half-spin fields with various boundary conditions in $d=5$ and $d=7$.

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arXiv2017

Towards Deconstruction of the Type D (2,0) Theory

We propose a four-dimensional supersymmetric theory that deconstructs, in a particular limit, the six-dimensional $(2,0)$ theory of type $D_k$. This 4d theory is defined by a necklace quiver with alternating gauge nodes $\mathrm{O}(2k)$ and $\mathrm{Sp}(k)$. We test this proposal by comparing the 6d half-BPS index to the Higgs branch Hilbert series of the 4d theory. In the process, we overcome several technical difficulties, such as Hilbert series calculations for non-complete intersections, and the choice of $\mathrm{O}$ versus $\mathrm{SO}$ gauge groups. Consistently, the result matches the Coulomb branch formula for the mirror theory upon reduction to 3d.

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arXiv2017

Large $N$ correlation functions in $\mathcal{N}=2$ superconformal quivers

Using supersymmetric localization, we consider four-dimensional $\mathcal{N}=2$ superconformal quiver gauge theories obtained from $\mathbb{Z}_n$ orbifolds of $\mathcal{N}=4$ Super Yang-Mills theory in the large $N$ limit at weak coupling. In particular, we show that: 1) The partition function for arbitrary couplings can be constructed in terms of universal building blocks. 2) It can be computed in perturbation series, which converges uniformly for $|λ_I|<π^2$, where $λ_I$ are the 't Hooft coupling of the gauge groups. 3) The perturbation series for two-point functions can be explicitly computed to arbitrary orders. There is no universal effective coupling by which one can express them in terms of correlators of the $\mathcal{N}=4$ theory. 4) One can define twisted and untwisted sector operators. At the perturbative orbifold point, when all the couplings are the same, the correlators of untwisted sector operators coincide with those of $\mathcal{N}=4$ Super Yang-Mills theory. In the twisted sector, we find remarkable cancellations of a certain number of planar loops, determined by the conformal dimension of the operator.

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arXiv2016

The NS limit of the 5D Superconformal Index

We consider the Nekrasov-Shatashvili (NS) limit of the five-dimensional superconformal index and propose a novel prescription for selecting the finite contributions. Applying the latter to various examples of U(1) theories, we find that the 5D NS index can be reproduced using recent techniques of Córdova and Shao, who related the 4D Schur index to the BPS spectrum of the theory on the Coulomb branch. In this picture, the 5D instanton solitons are interpreted as additional flavour nodes in an associated 5D BPS quiver.

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arXiv2016

Operator Mixing in Large $N$ Superconformal Field Theories on $\mathbb{S}^4$ and Correlators with Wilson loops

We find a general formula for the operator mixing on the $\mathbb{S}^4$ of chiral primary operators (CPO) for the ${\cal N}=4$ theory at large $N$ in terms of Chebyshev polynomials. As an application, we compute the correlator of a CPO and a Wilson loop, reproducing an earlier result by Giombi and Pestun obtained from a two-matrix model proposal. Finally, we discuss a simple method to obtain correlators in general ${\cal N}=2$ superconformal field theories in perturbation theory in terms of correlators of the ${\cal N}=4$ theory.

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arXiv2016

Large N Correlation Functions in Superconformal Field Theories

We compute correlation functions of chiral primary operators in N=2 superconformal theories at large N using a construction based on supersymmetric localization recently developed by Gerchkovitz et al. We focus on N=4 SYM as well as on superconformal QCD. In the case of N=4 we recover the free field theory results as expected due to non-renormalization theorems. In the case of superconformal QCD we study the planar expansion in the large N limit. The final correlators admit a simple generalization to a finite N formula which exactly matches the various small $N$ results in the literature.

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