arXiv subjects

Jorge G. Russo

Publications and source records attributed to Jorge G. Russo.

At least 37 records · Page 2Linked to original sources

arXiv2023

Nonlinear Electrodynamics without Birefringence

All solutions of the no-birefringence conditions for nonlinear electrodynamics are found. In addition to the known Born-Infeld and Plebanski cases, we find a ``reverse Born-Infeld'' case, which has a limit to Plebanski, and an ``extreme-Born-Infeld'' case, which arises as a Lagrangian constraint. Only Born-Infeld has a weak-field limit, and only Born-Infeld and extreme-Born Infeld avoid superluminal propagation in constant electromagnetic backgrounds, but all cases have a conformal strong-field limit that coincides with the strong-field limit of Born-Infeld found by Bialynicki-Birula.

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arXiv2020

Phases of unitary matrix models and lattice QCD2

We investigate the different large $N$ phases of a generalized Gross-Witten-Wadia $U(N)$ matrix model. The deformation mimics the one-loop determinant of fermion matter with a particular coupling to gauge fields. In one version of the model, the GWW phase transition is smoothed out and it becomes a crossover. In another version, the phase transition occurs along a critical line in the two-dimensional parameter space spanned by the 't~Hooft coupling $λ$ and the Veneziano parameter $τ$. We compute the expectation value of Wilson loops in both phases, showing that the transition is third-order. A calculation of the $β$ function shows the existence of an IR stable fixed point.

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arXiv2020

Deformed Cauchy random matrix ensembles and large $N$ phase transitions

We study a new hermitian one-matrix model containing a logarithmic Penner's type term and another term, which can be obtained as a limit from logarithmic terms. For small coupling, the potential has an absolute minimum at the origin, but beyond a certain value of the coupling the potential develops a double well. For a higher critical value of the coupling, the system undergoes a large $N$ third-order phase transition.

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arXiv2020

Displaced orbits and electric-magnetic black hole binaries

In presence of magnetic fields, the orbits of charged particles can be displaced from the equatorial plane. We study circular orbits of electrically charged massive objects around a magnetic black hole in the probe approximation. We show that there exist a one-parameter family of circular orbits at constant polar angle $θ$ and constant radius $r$, parameterized by the angular momentum. The angle $θ$ can be made arbitrarily small by increasing the charge-to-mass ratio of the orbiting particle, but when this is a Reissner-Nordstr\" om black hole, the condition $q\leq m$ implies that orbits exist only for $|θ-\fracπ{2}|< {\rm arccot}(2\sqrt{2})$. We show that the circular orbits are stable under small perturbations in the $θ$ and $r$ directions. We also discuss the Newtonian approximation and a binary system of electric and magnetic black holes, each one describing a circular orbit with no central force.

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arXiv2020

Multiple phases in a generalized Gross-Witten-Wadia matrix model

We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed Cauchy ensemble. Exact formulas for the partition function and Wilson loops are given in terms of Toeplitz determinants and minors and large $N$ results are obtained by using Szegö theorem with a Fisher-Hartwig singularity. In the large $N$ (planar) limit with two scaled couplings, the theory exhibits a surprisingly intricate phase structure in the two-dimensional parameter space.

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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

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

N = 2* Phase Transitions and Holography

We clarify the relationship between probe analysis of the supergravity dual and the large-N solution of the localization matrix model for the planar N = 2* super-Yang-Mills theory. A formalism inspired by supergravity allows us to systematically solve the matrix model at strong coupling. Quite surprisingly, we find that quantum phase transitions, known to occur in the N = 2* theory, start to be visible at the third order of the strong-coupling expansion and thus constitute a perturbative phenomenon on the string worldsheet.

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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

Exact gravitational plane waves and two-dimensional gravity

We discuss dynamical aspects of gravitational plane waves in Einstein theory with massless scalar fields. The general analytic solution describes colliding gravitational waves with constant polarization, which interact with scalar waves and, for generic initial data, produce a spacetime singularity at the focusing hypersurface. There is, in addition, an infinite family of regular solutions and an intriguing static geometry supported by scalar fields. Upon dimensional reduction, the theory can be viewed as an exactly solvable two-dimensional gravity model. This provides a new viewpoint on the gravitational dynamics. Finally, we comment on a simple mechanism by which short-distance corrections in the two-dimensional model can remove the singularity.

gr-qc↗

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 $d=7$.

hep-th↗

arXiv2017

Quantum phase transition in many-flavor supersymmetric QED$_{3}$

We study $\mathcal{N}=4$ supersymmetric QED in three dimensions, on a three-sphere, with 2N massive hypermultiplets and a Fayet-Iliopoulos parameter. We identify the exact partition function of the theory with a conical (Mehler) function. This implies a number of analytical formulas, including a recurrence relation and a second-order differential equation, associated with an integrable system. In the large N limit, the theory undergoes a second-order phase transition on a critical line in the parameter space. We discuss the critical behavior and compute the two-point correlation function of a gauge invariant mass operator, which is shown to diverge as one approaches criticality from the subcritical phase. Finally, we comment on the asymptotic 1/N expansion and on mirror symmetry.

hep-th↗

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

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

D branes in background fluxes and Nielsen-Olesen instabilities

In quantum field theory, charged particles with spin $\geq 1$ may become tachyonic in the present of magnetic fluxes above some critical field, signaling an instability of the vacuum. The phenomenon is generic, in particular, similar instabilities are known to exist in open and closed string theory, where a spinning string state can become tachyonic above a critical field. In compactifications involving RR fluxes $F_{p+2}$, the quantum states which could become tachyonic by the same Nielsen-Olesen mechanism are Dp branes. By constructing an appropriate background with RR magnetic flux that takes into account back-reaction, we identify the possible tachyonic Dp brane states and compute the formula for the energy spectrum in a sector. More generally, we argue that in any background RR magnetic flux, there are high spin Dp quantum states which become very light at critical fields.

hep-th↗

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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