arXiv subjects

Adrian R. Lugo

Publications and source records attributed to Adrian R. Lugo.

17 recordsLinked to original sources

arXiv2023

Holographic thermal propagator for arbitrary scale dimensions

Using the AdS/CFT correspondence we model the behaviour of the two point correlator of an operator with arbitrary scale dimension $Δ$ in arbitrary spacetime dimension $d$ for small but non-zero temperature. The obtained propagator coincides in the low temperature regime with the known result for $d=4$ for large $Δ$ at the order $T^d$ as well as with the $T^d$ and $T^{2d}$ terms of the exact all order result for $d=2$. Furthermore, for arbitrary $d$ we explicitly write down the expression for the order $T^{d}$ of the propagator for arbitrary $Δ$, and present a conjecture for the order $T^{2d}$ in the large $Δ$ limit.

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arXiv2015

Holographic phase transitions from higgsed, non abelian charged black holes

We find solutions of a gravity-Yang-Mills-Higgs theory in four dimensions that represent asymptotic anti-de Sitter charged black holes with partial/full gauge symmetry breaking. We then apply the AdS/CFT correspondence to study the strong coupling regime of a $2+1$ quantum field theory at temperature $T$ and finite chemical potential, which undergoes transitions to phases exhibiting the condensation of a composite charged vector operator below a critical temperature $T_c$, presumably describing $p+ip/p$-wave superconductors. In the case of $p+ip$-wave superconductors the transitions are always of second order. But for $p$-wave superconductors we determine the existence of a critical value $α_c$ of the gravitational coupling (for fixed Higgs v.e.v. parameter $\hat m_W$) beyond which the transitions become of first order. As a by-product, we show that the $p$-wave phase is energetically favored over the $p+ip$ one, for any values of the parameters. We also find the ground state solutions corresponding to zero temperature. Such states are described by domain wall geometries that interpolate between $AdS_4$ spaces with different light velocities, and for a given $\hat m_{W}$, they exist below a critical value of the coupling. The behavior of the order parameter as function of the gravitational coupling near the critical coupling suggests the presence of second order quantum phase transitions. We finally study the dependence of the solution on the Higgs coupling, and find the existence of a critical value beyond which no condensed solution is present.

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arXiv2013

Scalar potentials, propagators and global symmetries in AdS/CFT

We study the transition of a scalar field in a fixed $AdS_{d+1}$ background between an extremum and a minimum of a potential. We first prove that two conditions must be met for the solution to exist. First, the potential involved cannot be generic, i.e. a fine-tuning of their parameters is mandatory. Second, at least in some region its second derivative must have a negative upper limit which depends only on the dimensionality $d$. We then calculate the boundary propagator for small momenta in two different ways: first in a WKB approximation, and second with the usual matching method, generalizing the known calculation to arbitrary order. Finally, we study a system with spontaneously broken non-Abelian global symmetry, and show in the holographic language why the Goldstone modes appear.

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arXiv2013

On the matching method and the Goldstone theorem in holography

We study the transition of a scalar field in a fixed $AdS_{d+1}$ background between an extremum and a minimum of a potential. We compute analytically the solution to the perturbation equation for the vev deformation case by generalizing the usual matching method to higher orders and find the propagator of the boundary theory operator defined through the AdS-CFT correspondence. We show that, contrary to what happens at the leading order of the matching method, the next-to-leading order presents a simple pole at $q^2=0$ in accordance with the Goldstone theorem applied to a spontaneously broken dilatation invariance.

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arXiv2012

Spontaneous breaking of a discrete symmetry and holography

We present an exactly solvable model of a scalar field in an AdS$_{d+1}$ like background interpolating between a $Z_2$ preserving and a $Z_2$ breaking minima of the potential. We define its holographic dual through the AdS/CFT dictionary and argue that at zero temperature the $d-$dimensional strongly coupled system on the boundary of AdS$_{d+1}$ exhibits a phase with a spontaneously broken discrete symmetry. In the presence of a black hole in the bulk ($T\neq 0$) we find that, although the metastable phase is present, the discrete symmetry gets restored. We compute exactly the lowest order boundary correlation functions in the spontaneously broken phase at T=0, finding out a pole of the propagator for zero momenta that signals the presence of a massless mode.

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arXiv2010

Holography and $AdS_4$ self-gravitating dyons

We present a self-gravitating dyon solution of the Einstein-Yang-Mills-Higgs equations of motion in asymptotically AdS space. The back reaction of gauge and Higgs fields on the space-time geometry leads to the metric of an asymptotically AdS black hole. Using the gauge/gravity correspondence we analyze relevant properties of the finite temperature quantum field theory defined on the boundary. In particular we identify an order operator, characterize a phase transition of the dual theory on the border and also compute the expectation value of the finite temperature Wilson loop.

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arXiv2009

Tensionless supersymmetric M2 branes in $AdS_4 \times S^7$ and Giant Diabolo

We find various supersymmetric configurations of toroidal M2 brane solutions in $\AdS_4 \times S^7$ or, more generally, in $\AdS_4 \times S^7/Z_k$. In this class we identify solutions preserving 1/4 and 1/8 supersymmetries of the background. The supersymmetric M2 branes have angular momenta and winding on $S^7$, and null world-volumes. In certain cases they collapse to string-like configurations. These configurations can be viewed as a higher-dimensional (membrane) analog of BMN states. We compute the energy and angular momenta, showing that all supersymmetric configurations obey the BPS relation $E=J/R $,\ $J= \sum_{i=1}^4 |J_i|$ with $E, J\to \infty $. Finally, we also study another class of supersymmetric M2-branes, including uncompact rotating membranes of "diabolo" shape.

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arXiv2007

On supersymmetric $D6$-$\bar D 6$ systems with magnetic fields

We study systems of $D6$ and $\bar D 6$ branes with non zero world-volume magnetic fields in the weak coupling limit. We find two configurations for which the conditions for absence of tachyons in the spectra coincide exactly with those found in the low energy effective theory approach, for the systems to preserve 1/8 of the supersymmetries of the Type $IIA$ string theory vacuum. These conditions give rise to a four-parameter family of solutions in each case. We present further evidence of the stability of these systems by computing the lowest order interaction amplitude, verifying the no force condition as well as the supersymmetric character of the spectrum.

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arXiv2006

The fundamental non critical string

We obtain the (super) gravity solution in arbitrary space-time dimension less than ten, that gives a low energy description of a fundamental string embedded in a non critical vacuum, product of $d$-dimensional Minkowski space-time and a cigar-like geometry with scale $r_0$. This solution, one of the few known examples of objects doubly localized, both at the origin of the transverse space as well as at the tip of the cigar, is determined by its charge $Q$ under the Kalb-Ramond gauge field $B$, and presumably preserves, for even $d$, $2^\frac{d}{2}$ supercharges. Moreover, we show that the solution is reliable at least in a region far away from both origins, as it is the case with the well known branes of critical string theory.

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arXiv2004

About the stability of a D4 - anti D 4 system

We study a system of coincident $D4$ and $\bar D 4$ branes with non zero world-volume magnetic fields in the weak coupling limit. We show that the conditions for absence of tachyons in the spectrum coincide exactly with those found in hep-th/0206041, in the low energy effective theory approach, for the system to preserve a $\frac 14$ of the supersymmetries of the Type IIA string theory vacuum. We present further evidence about the stability of the system by computing the lowest order interaction amplitude from both open and closed channels, thus verifying the no force condition as well as the supersymmetric character of the spectrum. A brief discussion of the low energy effective five dimensional world-volume theory is given.

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arXiv1999

Non standard parametrizations and adjoint invariants of classical groups

We obtain local parametrizations of classical non-compact Lie groups where adjoint invariants under maximal compact subgroups are manifest. Extension to non compact subgroups is straightforward. As a by-product parametrizations of the same type are obtained for compact groups. They are of physical interest in any theory gauge invariant under the adjoint action, typical examples being the two dimensional gauged Wess-Zumino-Witten-Novikov models where these coordinatizations become of extreme usefulness to get the background fields representing the vacuum expectation values of the massless modes of the associated (super) string theory.

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arXiv1999

Monopole and Dyon Solutions in AdS space

We consider monopole and dyon classical solutions of the Yang-Mills-Higgs system coupled to gravity in asymptotically anti-de Sitter space. We discuss both singular and regular solutions to the second order equations of motion showing that singular Wu-Yang like dyons can be found, the resulting metric being of the Reissner-Nördstrom type (with cosmological constant). Concerning regular solutions, we analyze the conditions under which they can be constructed discussing, for vanishing coupling constant, the main distinctive features related to the anti-de Sitter asymptotic condition; in particular, we find in this case that the v.e.v. of the Higgs scalar, $|\vec H(\infty)|$, should be quantized in units of the natural mass scale $1/e r_0$ (related to the cosmological constant) according to $|\vec H(\infty)|^2 = m(m+1) (e r_0 )^{-2}$, with $m \in Z$.

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arXiv1999

Non linear realizations of isometry groups, conformal algebras and geodesics in Anti-de Sitter like spaces

We present the explicit global realization of the isometries of anti-de Sitter like spaces of signature $(d_-,d_+)$, and their algebras in the space of functions on the pseudo-Riemannian symmetric space $SO(d_- +1,d_+) / SO(d_-,d_+)$. The process of going to the invariant boundaries leads to the realization of the corresponding conformal groups and algebras. We compute systematically the geodesics in these spaces by considering the coset representation of them.

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arXiv1997

A N-extended version of superalgebras in D=3,9 mod 8

A set of generalized superalgebras containing arbitrary tensor p-form operators is considered in dimensions $D=2n+1$ for $n=1,4 mod 4$ and the general conditions for its existence expressed in the form of generalized Jacobi identities is established. These are then solved in a univoque way and some lowest dimensional cases $ D= 3, 9, 11 $ of possible interest are made explicit.

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arXiv1997

Exact monopole instantons and cosmological solutions in string theory from abelian dimensional reduction

We compute the exact string vacuum backgrounds corresponding to the non-compact coset theory $SU(2,1)/SU(2)$. The conformal field theory defined by the level $k= 4$ results in a five dimensional singular solution that factorizes in an asymptotic region as the linear dilaton solution and a $S^3$ model. It presents two abelian compact isometries that allow to reinterpreting it from a four dimensional point of view as a stationary and magnetically charged space-time resembling in some aspects the Kerr-Newman solution of general relativity. The $k=\frac{13}{7}$ theory on the other hand describes a cosmological solution that interpolates between a singular phase at short times and a $S^1 \times S^2$ universe after some planckian times.

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arXiv1997

SO(3) \times U(1) isometric instantons with non abelian hair in four dimensional string theory

We compute the exact effective string vacuum backgrounds of the level $k = 81/19 SU(2,1)/U(1)$ coset model. A compact SU(2) isometry present in this seven dimensional solution allows to interpreting it after compactification as a four dimensional non-abelian SU(2) charged instanton with a singular submanifold and an $SO(3) \times U(1)$ isometry. The semiclassical backgrounds, solutions of the type II strings, present similar characteristics.

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arXiv1992

Comments on Gauged WZW Models

Some remarks are made about free anomaly groups in gauged WZW models. Considering a quite general action, anomaly cancellation is analyzed. The possibility of gauging left and right sectors independently in some cases is remarked. In particular Toda theories can be seen as such a kind of models.

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