arXiv subjects

Márk Mezei

Publications and source records attributed to Márk Mezei.

50 records · Page 3Linked to original sources

arXiv2016

Scaling dimensions of monopole operators in the $\mathbb{CP}^{N_b - 1}$ theory in $2+1$ dimensions

We study monopole operators at the conformal critical point of the $\mathbb{CP}^{N_b - 1}$ theory in $2+1$ spacetime dimensions. Using the state-operator correspondence and a saddle point approximation, we compute the scaling dimensions of these operators to next-to-leading order in $1/N_b$. We find remarkable agreement between our results and numerical studies of quantum antiferromagnets on two-dimensional lattices with SU($N_b$) global symmetry, using the mapping of the monopole operators to valence bond solid order parameters of the lattice antiferromagnet.

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arXiv2015

Three-sphere free energy for classical gauge groups

In this note, we calculate the $S^3$ free energy $F$ of 3-d ${\cal N}\geq 4$ supersymmetric gauge theories with $U(N)$, $O(N)$, and $USp(2N)$ gauge groups and matter hypermultiplets in the fundamental and two-index tensor representations. Supersymmetric localization reduces the computation of $F$ to a matrix model that we solve in the large $N$ limit using two different methods. The first method is a saddle point approximation first introduced in arXiv:1011.5487, which we extend to next-to-leading order in $1/N$. The second method generalizes the Fermi gas approach of arXiv:1110.4066 to theories with symplectic and orthogonal gauge groups, and yields an expression for $F$ valid to all orders in $1/N$. In developing the second method, we use a non-trivial generalization of the Cauchy determinant formula.

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arXiv2015

Entanglement entropy across a deformed sphere

I study the entanglement entropy (EE) across a deformed sphere in conformal field theories (CFTs). I show that the sphere (locally) minimizes the universal term in EE among all shapes. In arXiv:1407.7249 it was derived that the sphere is a local extremum, by showing that the contribution linear in the deformation parameter is absent. In this paper I demonstrate that the quadratic contribution is positive and is controlled by the coefficient of the stress tensor two point function, $C_T$. Such a minimization result contextualizes the fruitful relation between the EE of a sphere and the number of degrees of freedom in field theory. I work with CFTs with gravitational duals, where all higher curvature couplings are turned on. These couplings parametrize conformal structures in stress tensor $n$-point functions, hence I show the result for infinitely many CFT examples.

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arXiv2015

Some results on the shape dependence of entanglement and Rényi entropies

We study how the universal contribution to entanglement entropy in a conformal field theory depends on the entangling region. We show that for a deformed sphere the variation of the universal contribution is quadratic in the deformation amplitude. We generalize these results for Rényi entropies. We obtain an explicit expression for the second order variation of entanglement entropy in the case of a deformed circle in a three dimensional CFT with a gravity dual. For the same system, we also consider an elliptic entangling region and determine numerically the entanglement entropy as a function of the aspect ratio of the ellipse. Based on these three-dimensional results and Solodukhin's formula in four dimensions, we conjecture that the sphere minimizes the universal contribution to entanglement entropy in all dimensions.

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arXiv2014

Quantum phase transitions in semi-local quantum liquids

We consider several types of quantum critical phenomena from finite-density gauge-gravity duality which to different degrees lie outside the Landau-Ginsburg-Wilson paradigm. These include: (1) a "bifurcating" critical point, for which the order parameter remains gapped at the critical point, and thus is not driven by soft order parameter fluctuations. Rather it appears to be driven by "confinement" which arises when two fixed points annihilate and lose conformality. On the condensed side, there is an infinite tower of condensed states and the nonlinear response of the tower exhibits an infinite spiral structure; (2) a "hybridized" critical point which can be described by a standard Landau-Ginsburg sector of order parameter fluctuations hybridized with a strongly coupled sector; (3) a "marginal" critical point which is obtained by tuning the above two critical points to occur together and whose bosonic fluctuation spectrum coincides with that postulated to underly the "Marginal Fermi Liquid" description of the optimally doped cuprates.

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arXiv2013

Probing renormalization group flows using entanglement entropy

In this paper we continue the study of renormalized entanglement entropy introduced in [1]. In particular, we investigate its behavior near an IR fixed point using holographic duality. We develop techniques which, for any static holographic geometry, enable us to extract the large radius expansion of the entanglement entropy for a spherical region. We show that for both a sphere and a strip, the approach of the renormalized entanglement entropy to the IR fixed point value contains a contribution that depends on the whole RG trajectory. Such a contribution is dominant, when the leading irrelevant operator is sufficiently irrelevant. For a spherical region such terms can be anticipated from a geometric expansion, while for a strip whether these terms have geometric origins remains to be seen.

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arXiv2013

Monopole Taxonomy in Three-Dimensional Conformal Field Theories

We study monopole operators at the infrared fixed points of Abelian and non-Abelian gauge theories with N_f fermion flavors in three dimensions. At large N_f, independent monopole operators can be defined via the state-operator correspondence only for stable monopole backgrounds. In Abelian theories, every monopole background is stable. In the non-Abelian case, we find that many (but not all) backgrounds are stable in each topological class. We calculate the infrared scaling dimensions of the corresponding operators through next-to-leading order in 1/N_f. In the case of U(N_c) QCD with N_f fundamental fermions (and in particular in the QED case, N_c =1), we find that the monopole operators transform as non-trivial irreducible representations of the SU(N_f) flavor symmetry group.

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arXiv2011

Lectures on holographic non-Fermi liquids and quantum phase transitions

In these lecture notes we review some recent attempts at searching for non-Fermi liquids and novel quantum phase transitions in holographic systems using gauge/gravity duality. We do this by studying the simplest finite density system arising from the duality, obtained by turning on a nonzero chemical potential for a U(1) global symmetry of a CFT, and described on the gravity side by a charged black hole. We address the following questions of such a finite density system: 1. Does the system have a Fermi surface? What are the properties of low energy excitations near the Fermi surface? 2. Does the system have an instability to condensation of scalar operators? What is the critical behavior near the corresponding quantum critical point? We find interesting parallels with those of high T_c cuprates and heavy electron systems. Playing a crucial role in our discussion is a universal intermediate-energy phase, called a "semi-local quantum liquid", which underlies the non-Fermi liquid and novel quantum critical behavior of a system. It also provides a novel mechanism for the emergence of lower energy states such as a Fermi liquid or a superconductor.

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arXiv2010

Boson stars and oscillatons in an inflationary universe

Spherically symmetric gravitationally bound, oscillating scalar lumps (boson stars and oscillatons) are considered in Einstein's gravity coupled to massive scalar fields in 1+D dimensional de Sitter-type inflationary space-times. We show that due to inflation bosons stars and oscillatons lose mass through scalar radiation, but at a rate that is exponentially small when the expansion rate is slow.

gr-qc↗

arXiv2010

Mass loss and longevity of gravitationally bound oscillating scalar lumps (oscillatons) in D-dimensions

Spherically symmetric oscillatons (also referred to as oscillating soliton stars) i.e. gravitationally bound oscillating scalar lumps are considered in theories containing a massive self-interacting real scalar field coupled to Einstein's gravity in 1+D dimensional spacetimes. Oscillations are known to decay by emitting scalar radiation with a characteristic time scale which is, however, extremely long, it can be comparable even to the lifetime of our universe. In the limit when the central density (or amplitude) of the oscillaton tends to zero (small-amplitude limit) a method is introduced to compute the transcendentally small amplitude of the outgoing waves. The results are illustrated in detail on the simplest case, a single massive free scalar field coupled to gravity.

gr-qc↗

arXiv2010

Quantum phase transitions in holographic models of magnetism and superconductors

We study a holographic model realizing an "antiferromagnetic" phase in which a global SU(2) symmetry representing spin is broken down to a U(1) by the presence of a finite electric charge density. This involves the condensation of a neutral scalar field in a charged AdS black hole. We observe that the phase transition for both neutral and charged (as in the standard holographic superconductor) order parameters can be driven to zero temperature by a tuning of the UV conformal dimension of the order parameter, resulting in a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type. We also characterize the antiferromagnetic phase and an externally forced ferromagnetic phase by showing that they contain the expected spin waves with linear and quadratic dispersions respectively.

hep-th↗

arXiv2009

Oscillons in dilaton-scalar theories

It is shown by both analytical methods and numerical simulations that extremely long living spherically symmetric oscillons appear in virtually any real scalar field theory coupled to a massless dilaton (DS theories). In fact such "dilatonic" oscillons are already present in the simplest non-trivial DS theory -- a free massive scalar field coupled to the dilaton. It is shown that in analogy to the previously considered cases with a single nonlinear scalar field, in DS theories there are also time periodic quasibreathers (QB) associated to small amplitude oscillons. Exploiting the QB picture the radiation law of the small amplitude dilatonic oscillons is determined analytically.

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arXiv2009

Radiation of scalar oscillons in 2 and 3 dimensions

The radiation loss of small-amplitude radially symmetric oscillons (long-living, spatially localized, time-dependent solutions) in two- and three-dimensional scalar field theories is computed analytically in the small-amplitude expansion. The amplitude of the radiation is beyond all orders in perturbation theory and it is determined using matched asymptotic series expansions and Borel summation. The general results are illustrated on the case of the two- and three-dimensional sine-Gordon theory and a two-dimensional $ϕ^6$ model. The analytic predictions are found to be in good agreement with the results of numerical simulations of oscillons.

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arXiv2008

Computation of the radiation amplitude of oscillons

The radiation loss of small amplitude oscillons (very long-living, spatially localized, time dependent solutions) in one dimensional scalar field theories is computed in the small-amplitude expansion analytically using matched asymptotic series expansions and Borel summation. The amplitude of the radiation is beyond all orders in perturbation theory and the method used has been developed by Segur and Kruskal in Phys. Rev. Lett. 58, 747 (1987). Our results are in good agreement with those of long time numerical simulations of oscillons.

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