arXiv subjects

J. Erdmenger

Publications and source records attributed to J. Erdmenger.

12 recordsLinked to original sources

arXiv2015

Holographic impurities and Kondo effect

Magnetic impurities are responsible for many interesting phenomena in condensed matter systems, notably the Kondo effect and quantum phase transitions. Here we present a holographic model of a magnetic impurity that captures the main physical properties of the large-spin Kondo effect. We estimate the screening length of the Kondo cloud that forms around the impurity from a calculation of entanglement entropy and show that our results are consistent with the g-theorem.

hep-th↗

arXiv2014

QCD and strongly coupled gauge theories: challenges and perspectives

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly-coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.

hep-ph↗

arXiv2005

Spectral Flow on the Higgs Branch and AdS/CFT Duality

We use AdS/CFT duality to study the large N_c limit of the meson spectrum on the Higgs branch of a strongly coupled, N=2 supersymmetric SU(N_c) gauge theory with N_f =2 fundamental hypermultiplets. In the dual supergravity description, the Higgs branch is described by SU(2) instanton configurations on D7-branes in an AdS background. We compute the spectral flow parameterized by the size of a single instanton. In the large N_c limit, there is a sense in which the flow from zero to infinite instanton size, or Higgs VEV, can be viewed as a closed loop. We show that this flow leads to a non-trivial rearrangement of the spectrum.

hep-th↗

arXiv2003

A Gravity Dual of Chiral Symmetry Breaking

We establish a holographic description of chiral symmetry breaking for a particular confining large N non-supersymmetric gauge theory with matter in the fundamental representation. The gravity dual of this theory is obtained by introducing a D7-brane probe into a deformed Anti-de Sitter background found by Constable and Myers. We numerically compute the \barψψcondensate and meson spectrum by solving the equation of motion of the D7-brane probe in this background. We find a symmetry breaking condensate as well as the associated, pion-like, Goldstone boson in the limit of small quark mass. The existence of the condensate ensures that the D7-brane never reaches the naked singularity at the origin of the deformed AdS space.

hep-th↗

arXiv2003

Chiral Symmetry Breaking and Pions in Non-Supersymmetric Gauge/Gravity Duals

We study gravity duals of large N non-supersymmetric gauge theories with matter in the fundamental representation by introducing a D7-brane probe into deformed AdS backgrounds. In particular, we consider a D7-brane probe in both the AdS Schwarzschild black hole solution and in the background found by Constable and Myers, which involves a non-constant dilaton and S^5 radius. Both these backgrounds exhibit confinement of fundamental matter and a discrete glueball and meson spectrum. We numerically compute the quark condensate and meson spectrum associated with these backgrounds. In the AdS-black hole background, a quark-bilinear condensate develops only at non-zero quark mass. We speculate on the existence of a third order phase transition at a critical quark mass where the D7 embedding undergoes a geometric transition. In the Constable-Myers background, we find a chiral symmetry breaking condensate as well as the associated Goldstone boson in the limit of small quark mass. The existence of the condensate ensures that the D7-brane never reaches the naked singularity at the origin of the deformed AdS space.

hep-th↗

arXiv2002

(De)constructing Intersecting M5-branes

We describe intersecting M5-branes, as well as M5-branes wrapping the holomorphic curve xy=c, in terms of a limit of a defect conformal field theory with two-dimensional (4,0) supersymmetry. This dCFT describes the low-energy theory of intersecting D3-branes at a C^2/Z_k orbifold. In an appropriate k -> infinity limit, two compact spatial directions are generated. By identifying moduli of the M5-M5 intersection in terms of those of the dCFT, we argue that the SU(2)_L R-symmetry of the (4,0) defect CFT matches the SU(2) R-symmetry of the N =2, d=4 theory of the M5-M5 intersection. We find a 't Hooft anomaly in the SU(2)_L R-symmetry, suggesting that tensionless strings give rise to an anomaly in the SU(2) R-symmetry of intersecting M5-branes.

hep-th↗

arXiv2000

Near-extremal correlators and vanishing supergravity couplings in AdS/CFT

We study near-extremal n-point correlation functions of chiral primary operators, in which the maximal scale dimension k is related to the others by k=\sum_i k_i-m with m equal to or smaller than n-3. Through order g^2 in field theory, we show that these correlators are simple sums of terms each of which factors into products of lower-point correlators. Terms which contain only factors of two- and three-point functions are not renormalized, but other terms have non-vanishing order g^2 corrections. We then show that the contributing AdS exchange diagrams neatly match this factored structure. In particular, for n=4,5 precise agreement in form and coefficient is established between supergravity and the non-renormalized factored terms from field theory. On the other hand, contact diagrams in supergravity would produce a non-factored structure. This leads us to conjecture that the corresponding bulk couplings vanish, so as to achieve full agreement between the structure of these correlators in supergravity and weak-coupling field theory.

hep-th↗

arXiv2000

Non-renormalization of next-to-extremal correlators in N=4 SYM and the AdS/CFT correspondence

We show that next-to-extremal correlators of chiral primary operators in N=4 SYM theory do not receive quantum corrections to first order in perturbation theory. Furthermore we consider next-to-extremal correlators within AdS supergravity. Here the exchange diagrams contributing to these correlators yield results of the same free-field form as obtained within field theory. This suggests that quantum corrections vanish at strong coupling as well.

hep-th↗

arXiv1999

Superconformal Transformation Properties of the Supercurrent II: Abelian Gauge Theories

We derive the superconformal transformation properties of the supercurrent for N=1 supersymmetric QED in four dimensions within the superfield formalism. Superconformal Ward identities for Green functions involving insertions of the supercurrent are conveniently derived by coupling the supercurrent to the appropriate prepotential of a classical curved superspace background, and by combining superdiffeomorphisms and super Weyl transformations. We determine all superconformal anomalies of SQED on curved superspace within an all-order perturbative approach and derive a local Callan-Symanzik equation. Particular importance is given to the issue of gauge invariance.

hep-th↗

arXiv1997

Conformally Covariant Differential Operators: Symmetric Tensor Fields

We extend previous work on conformally covariant differential operators to consider the case of second order operators acting on symmetric traceless tensor fields. The corresponding flat space Green function is explicitly constructed and shown to be in accord with the requirements of conformal invariance.

gr-qc↗

arXiv1997

Conformally Covariant Differential Operators: Properties and Applications

We discuss conformally covariant differential operators, which under local rescalings of the metric, δ_σg^{μν} = 2 σg^{μν}, transform according to δ_σΔ= r Δσ+ (s-r) σΔfor some r if Δis s-th order. It is shown that the flat space restrictions of their associated Green functions have forms which are strongly constrained by flat space conformal invariance. The same applies to the variation of the Green functions with respect to the metric. The general results are illustrated by finding the flat space Green function and also its first variation for previously found second order conformal differential operators acting on $k$-forms in general dimensions. Furthermore we construct a new second order conformally covariant operator acting on rank four tensors with the symmetries of the Weyl tensor whose Green function is similarly discussed. We also consider fourth order operators, in particular a fourth order operator acting on scalars in arbitrary dimension, which has a Green function with the expected properties. The results obtained here for conformally covariant differential operators are generalisations of standard results for the two dimensional Laplacian on curved space and its associated Green function which is used in the Polyakov effective gravitational action. It is hoped that they may have similar applications in higher dimensions.

hep-th↗

arXiv1996

Conserved Currents and the Energy Momentum Tensor in Conformally Invariant Theories for General Dimensions

The implications of conformal invariance, as relevant in quantum field theories at a renormalisation group fixed point, are analysed with particular reference to results for correlation functions involving conserved currents and the energy momentum tensor. Ward identities resulting from conformal invariance are discussed. Explicit expressions for two and three point functions, which are essentially determined by conformal invariance, are obtained. As special cases we consider the three point functions for two vector and an axial current in four dimensions, which realises the usual anomaly simply and unambiguously, and also for the energy momentum tensor in general dimension $d$. The latter is shown to have two linearly independent forms in which the Ward identities are realised trivially, except if $d = 4$, when the two forms become degenerate. This is necessary in order to accommodate the two independent forms present in the trace of the energy momentum tensor on curved space backgrounds for conformal field theories in four dimensions. The coefficients of the two trace anomaly terms are related to the three parameters describing the general energy momentum tensor three point function. The connections with gravitational effective actions depending on a background metric are described. A particular form due to Riegert is shown to be unacceptable. Conformally invariant expressions for the effective action in four dimensions are obtained using the Green function for a differential operator which has simple properties under local rescalings of the metric.

hep-th↗