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.Instituto de Física La Plat

CFT thermal 2-point function

This is a short review of our recent work [B. Bajc and A. R. Lugo, arXiv:2212.13639 [hep-th]] with some new original results. We numerically calculate the conformal two point correlation function of operators with arbitrary scale dimension up to order T2d in the low temperature expansion. We analytically compute its large scale dimension limit up to the same order.Fil: Bajc, Borut. Institut Jožef Stefan; EsloveniaFil: Lugo, Adrián René. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentin

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.Instituto de Física La Plat

On supersymmetric D6‒D6 systems with magnetic fields

We study systems of D6 and D6 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.Facultad de Ciencias ExactasInstituto de Física La Plat

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 symme-try 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 Tc, presumably describing p + ip/p-wave su-perconductors. 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 αTc of the gravitational coupling (for fixed Higgs v.e.v. parameter mW) 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 AdST4 spaces with different light velocities, and for a given mW, 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.Facultad de Ciencias ExactasInstituto de Física La Plat

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.Facultad de Ciencias Exacta

Correlation functions in the non-commutative Wess-Zumino-Witten model

We develop a systematic perturbative expansion and compute the one-loop two-points, three-points and four-points correlation functions in a non-commutative version of the U (N) Wess-Zumino-Witten model in different regimes of the θ-parameter showing in the first case a kind of phase transition around the value θc = √p2 + 4m2/(λ2p), where λ is a ultraviolet cut-off in a Schwinger regularization scheme. As a by-product we obtain the functions of the renormalization group, showing they are essentially the same as in the commutative case but applied to the whole U (N) fields; in particular there exists a critical point where they are null, in agreement with a recent background field computation of the beta-function, and the anomalous dimension of the Lie algebra-valued field operator agrees with the current algebra prediction. The non-renormalization of the level k is explicitly verified from the four-points correlator, where a left-right non-invariant counter-term is needed to render finite the theory, that it is however null on-shell. These results give support to the equivalence of this model with the commutative one. © 2001 Elsevier Science B.V.Instituto de Física La Plat

On supersymmetric D6‒D6 systems with magnetic fields

We study systems of D6 and D6 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.Facultad de Ciencias ExactasInstituto de Física La Plat

On supersymmetric Dp–Dp brane solutions

We analyze in the spirit of hep-th/0110039 the possible existence of supersymmetric Dp– D p brane systems in flat ten-dimensional Minkowski space. For p=3,4 we show that besides the solutions related by T-duality to the D2– D 2 systems found by Bak and Karch there exist other ansatz whose compatibility is shown from general arguments and that preserve also eight supercharges, in particular, a D4– D 4 system with D2-branes dissolved on it and Taub–NUT charge. We carry out the explicit construction in Weyl basis of the corresponding Killing spinors and conjecture the existence of new solutions for higher-dimensional branes with some compact directions analogous to the supertube recently found.Facultad de Ciencias Exacta

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

We compute the exact string vacuum backgrounds corresponding to the noncompact 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 an S3 model. It presents two Abelian compact isometries that allow us to reinterpret 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=13/7 theory, on the other hand, describes a cosmological solution that interpolates between a singular phase at short times and an S1xS2 universe after some Planckian times.Facultad de Ciencias Exacta