Wolfgang Mück

Holographic renormalization and Ward identities with the Hamilton–Jacobi method

Abstract A systematic procedure for performing holographic renormalization, which makes use of the Hamilton–Jacobi method, is proposed and applied to a bulk theory of gravity interacting with a scalar field and a U (1) gauge field in the Stuckelberg formalism. We describe how the power divergences are obtained as solutions of a set of “descent equations” stemming from the radial Hamiltonian constraint of the theory. In addition, we isolate the logarithmic divergences, which are closely related to anomalies. The method allows to determine also the exact one-point functions of the dual field theory. Using the other Hamiltonian constraints of the bulk theory, we derive the Ward identities for diffeomorphisms and gauge invariance. In particular, we demonstrate the breaking of U (1) R current conservation, recovering the holographic chiral anomaly recently discussed in hep-th/0112119 and hep-th/0202056 .

Bulk dynamics in confining gauge theories

Abstract We consider gauge/string duality (in the supergravity approximation) for confining gauge theories. The system under scrutiny is a 5-dimensional consistent truncation of type IIB supergravity obtained using the Papadopoulos–Tseytlin ansatz with boundary momentum added. We develop a gauge-invariant and sigma-model-covariant approach to the dynamics of 5-dimensional bulk fluctuations. For the Maldacena–Nunez subsystem, we study glueball mass spectra. For the Klebanov–Strassler subsystem, we compute the linearized equations of motion for the 7-scalar system, and show that a 3-scalar sector containing the scalar dual to the gluino bilinear decouples in the UV. We solve the fluctuation equations exactly in the “moderate UV” approximation and check this approximation numerically. Our results demonstrate the feasibility of analyzing the generally coupled equations for scalar bulk fluctuations, and constitute a step on the way towards computing correlators in confining gauge theories.

Glueballs vs. gluinoballs: Fluctuation spectra in non-AdS/non-CFT

Abstract Building on earlier results on holographic bulk dynamics in confining gauge theories, we compute the spin-0 and spin-2 spectra of the Maldacena–Nunez and Klebanov–Strassler theories, that have non-singular supergravity duals. We construct and apply a numerical recipe for computing mass spectra from certain determinants. In the Klebanov–Strassler case, the spectra of states containing the glueball and gluinoball are universal and quadratic in the supergravity approximation, i.e., their mass-squareds depend on consecutive number as m 2 ∼ n 2 for large n, with a universal proportionality constant. The hardwall approximation appears to work poorly when compared to the unique spectra we find in the full theory with a smooth cap-off in the infrared.

New results on holographic three-point functions

We exploit a gauge invariant approach for the analysis of the equations governing the dynamics of active scalar fluctuations coupled to the fluctuations of the metric along holographic RG flows. In the present approach, a second order ODE for the active scalar emerges rather simply and makes it possible to use the Greens function method to deal with (quadratic) interaction terms. We thus fill a gap for active scalar operators, whose three-point functions have been inaccessible so far, and derive a general, explicitly Bose symmetric formula thereof. As an application we compute the relevant three-point function along the GPPZ flow and extract the irreducible trilinear couplings of the corresponding superglueballs by amputating the external legs on-shell.

Consistent linearized gravity in brane backgrounds

Abstract A globally consistent treatment of linearized gravity in the Randall–Sundrum background with matter on the brane is formulated. Using a novel gauge, in which the transverse components of the metric are non-vanishing, the brane is kept straight. We analyze the gauge symmetries and identify the physical degrees of freedom of gravity. Our results underline the necessity for non-gravitational confinement of matter to the brane.

Geodesics and Newton's Law in Brane Backgrounds

In brane world models our universe is considered as a brane imbedded into a higher dimensional space. We discuss the behaviour of geodesics in the Randall-Sundrum background and point out that free massive particles cannot move along the brane only. The brane is repulsive, and matter will be expelled from the brane into the extra dimension. This is rather undesirable, and hence we study an alternative model with a non-compact extra dimension, but with an attractive brane embedded into the higher dimensional space. We study the linearized gravity equations and show that Newtons gravitational law is valid on the brane also in the alternative background.

Correlation functions in holographic renormalization group flows

Abstract We consider the holographic duality for a generic bulk theory of scalars coupled to gravity. By studying the fluctuations around Poincare invariant backgrounds with non-vanishing scalars, with the scalar and metric boundary conditions considered as being independent, we obtain all one- and two-point functions in the dual renormalization group flows of the boundary field theory. Operator and vev flows are explicitly distinguished by means of the physical condensates. The method is applied to the GPPZ and Coulomb branch flows, and field theoretical expectations are confirmed.

Spinor parallel propagator and Green function in maximally symmetric spaces

We introduce the spinor parallel propagator for maximally symmetric spaces in any dimension. Then, the Dirac spinor Green functions in the maximally symmetric spaces n , Sn and Hn are calculated in terms of intrinsic geometric objects. The results are covariant and coordinate independent.We introduce the spinor parallel propagator for maximally symmetric spaces in any dimension. Then, the Dirac spinor Green’s functions in the maximally symmetric spaces Rn, Sn and Hn are calculated in terms of intrinsic geometric objects. The results are covariant and coordinate-independent. ∗E-mail address: wmueck@sfu.ca

Gauge/String Duality

1 Dipartimento di Scienze Fisiche, Universita degli Studi di Napoli Federico II, INFN, Sezione di Napoli, Via Cintia, 80126 Napoli, Italy 2 Department of Physics, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, UK 3 Michigan Center for Theoretical Physics, The University of Michigan, Ann Arbor, MI 48109-1120, USA 4 Departamento de Fisica de Particulas, Instituto Galego de Fisica de Altas Energias (IGFAE), Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain 5 Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, 1040 Vienna, Austria 6 Department of Physics, Sofia University, 1504 Sofia, Bulgaria 7 Department of Physics, and IRMACS, Simon Fraser University, Burnaby, British Columbia, Canada

Towards Holographic Renormalization of Fake Supergravity

Abstract A step is made towards generalizing the method of holographic renormalization to backgrounds which are not asymptotically AdS, corresponding to a dual gauge theory which has logarithmically running couplings even in the ultraviolet. A prime example is the background of Klebanov–Strassler (KS). In particular, a recipe is given how to calculate renormalized two-point functions for the operators dual to the bulk scalars. The recipe makes use of gauge-invariant variables for the fluctuations around the background and works for any bulk theory of the fake supergravity type. It elegantly incorporates the renormalization scheme dependence of local terms in the correlators. Before applying the method to the KS theory, it is verified that known results in asymptotically AdS backgrounds are reproduced. Finally, some comments on the calculation of renormalized vacuum expectation values are made.