Ian I. Kogan

Effective Lagrangians and universality classes of nonlinear bigravity

We discuss the fully non-linear formulation of multigravity. The concept of universality classes of effective Lagrangians describing bigravity, which is the simplest form of multigravity, is introduced. We show that non-linear multigravity theories can naturally arise in several different physical contexts: brane configurations, certain Kaluza-Klein reductions and some non-commutative geometry models. The formal and phenomenological aspects of multigravity (including the problems linked to the linearized theory of massive gravitons) are briefly discussed.

Logarithmic operators and hidden continuous symmetry in critical disordered models

Abstract We study the model of (2 + 1)-dimensional relativistic fermions in a random non-Abelian gauge potential at criticality. The exact solution shows that the operator expansion contains a conserved current — a generator of a continuous symmetry. The presence of this operator changes the operator product expansion and gives rise to logarithmic contributions to the correlation functions at the critical point. We calculate the distribution function of the local density of states in this model and find that it follows the famous log-normal law.

The m→0 limit for massive graviton in dS4 and AdS4 — How to circumvent the van Dam–Veltman–Zakharov discontinuity

Abstract We show that, by considering physics in dS 4 or AdS 4 spacetime, one can circumvent the van Dam–Veltman–Zakharov theorem which requires that the extra polarization states of a massive graviton do not decouple in the massless limit. It is shown that the smoothness of the m →0 limit is ensured if the H (“Hubble”) parameter, associated with the horizon of the dS 4 or AdS 4 space, tends to zero slower than the mass of the graviton m .

A three three-brane universe: new phenomenology for the new millennium?

Abstract We consider an extension of the Randall–Sundrum model with three parallel 3-branes in a 5-dimensional spacetime. This new construction, apart from providing a solution to the Planck hierarchy problem, has the advantage that the SM fields are confined on a positive tension brane. The study of the phenomenology of this model reveals an anomalous first KK state which is generally much lighter than the remaining tower and also much more strongly coupled to matter. Bounds on the parameter space of the model can be placed by comparison of specific processes with the SM background as well as by the latest Cavendish experiments. The model suggests a further exotic possibility if one drops the requirement of solving the hierarchy problem. In this case gravity may result from the exchange of the ordinary graviton plus an ultralight KK state and modifications of gravity may occur at both small and extremely large scales.

D-brane recoil and logarithmic operators

Abstract We construct the pair of logarithmic operators associated with the recoil of a D -brane. This construction establishes a connection between a translation in time and a world-sheet rescaling. The problem of measuring the centre of mass coordinate of the D -brane is considered and the relation between the string uncertainty principle and the logarithmic operators is discussed.

On stringy thresholds in SYM/AdS thermodynamics

Abstract We consider aspects of the role of stringy scales and Hagedorn temperatures in the correspondence between various field theories and AdS-type spaces. The boundary theory is set on a toroidal world-volume to enable small scales to appear in the supergravity backgrounds also for low field-theory temperatures. We find that thermodynamical considerations tend to favour background manifolds with no string-size characteristic scales. The gravitational dynamics censors the reliable exposure of Hagedorn physics on the supergravity side, and the system does not allow the study of the Hagedorn scale by low-temperature field theories. These results are obtained following some heuristic assumptions on the character of stringy modifications to the gravitational backgrounds. A rich phenomenology appears on the supergravity side, with different string backgrounds dominating in different regions, which should have field-theoretic consequences. Six-dimensional world-volumes turn out to be borderline cases from several points of view. For lower-dimensional world-volumes, a fully holographic behaviour is exhibited to order 1/ N 2 , and open strings in their presence are found to have a thermodynamic Hagedorn behaviour similar to that of closed strings in flat space.

World-sheet logarithmic operators and target space symmetries in string theory

Abstract We discuss the target-space interpretation of the world-sheet logarithmic operators in string theory. These operators generate the normalizable zero modes (discrete states) in target space, which restore the symmetries of the theory broken by the background. The problem of the recoil in string theory is considered, as well as some general properties of string amplitudes containing logarithmic operators.

On the origin of W-algebras

Abstract We show that the complex and projective structures on 2D Riemann surfaces are determined by the solutions to the linear differential equations obtained by the hamiltonian reduction of Sl(2, C ) connections by the gauge parabolic subgroup. The compatibility of complex (μ) and projective (T) structures appears as the associated zero-curvature condition on the reduced symplectic manifold and is nothing but the conformal Ward identity. Generalizing this construction to the reduction of Sl (n, C ) connections by the maximal parabolic gauge subgroup, we obtain generalized complex (μ, ρ,…) and projective (T, W, …) structures. From their compatibility conditions we explicitly obtain the Ward identities of Wn-gravity and the operator product expansions of the Wn-algebras. The associated linear differential equations (one of which involves the basic differential operator of the nth reduction of the KP hierarchy) allow for a geometric interpretation of the W-symmetries in terms of deformations of flag configurations in the jet bundle γ(n−1). We also show how to derive the Wn-Ward identities fromt he quantization of the (2 + 1)-dimensional Chern-Simons theory.

Brane universe and multigravity: modification of gravity at large and small distances

Abstract We consider the modification of gravity at large distances in Brane Universes which was discussed recently [I.I. Kogan, S. Mouslopoulos, A. Papazoglou, G.G. Ross, J. Santiago, hep-ph/9912552; R. Gregory, V.A. Rubakov, S.M. Sibiryakov, hep-th/0002072; C. Csaki, J. Erlich, T.J. Hollowood, hep-th/0002161; G. Dvali, G. Gabadadze, M. Porrati, hep-th/0002190]. In these models the modification of gravity at large distances is connected to the existence of a negative tension brane(s) and an exponentially small tunneling factor. We discuss a general model which interpolates between the Bi-gravity +−+ model [I.I. Kogan, S. Mouslopoulos, A. Papazoglou, G.G. Ross, J. Santiago, hep-ph/9912552] and the GRS model [R. Gregory, V.A. Rubakov, S.M. Sibiryakov, hep-th/0002072]. We also discuss the possible mechanism of stabilization of negative tension branes in an AdS background. Finally we show that extra degrees of freedom of massive gravitons do not lead to a disastrous contradiction with General Relativity if the stabilization condition ∫ dy −G (5) (T μ μ −2T 5 5 )=0 [P. Kanti, I.I. Kogan, K.A. Olive, M. Pospelov, hep-ph/9912266] is implemented.

On gravitational dressing of 2D field theories in chiral gauge

Abstract After giving a pedagogical review of the chiral gauge approach to 2D gravity, with particular emphasis on the derivation of the gravitational Ward identities, we discuss in some detail the interpretation of matter correlation functions coupled to gravity in chiral gauge. We argue that in chiral gauge no explicit gravitational dressing factor, analogue to the Lionville exponential in conformal gauge, is necessary for left-right symmetric matter operators. In particular, we examine the gravitationally dressed four-point correlation function of products of left and right fermions. We solve the corresponding gravitational Ward identity exactly: in the presence of gravity this four-point function exhibits a logarithmic short-distance singularity, instead of the power-law singularity in the absence of gravity. This rather surprising effect is non-perturbative in the gravitational coupling and is a sign for logarithms in the gravitationally dressed operator product expansions. We also discuss some perturbative evidence that the chiral Gross-Neveu model may remain integrable when coupled to gravity.