Central charges and Lorentz and internal symmetries in massive supersymmetric quantum field theory

The properties of central charges in the framework of the massive supersymmetric quantum field theory related to internal symmetries, Lorentz covariance and locality of the fields are investigated. It is shown that in the presence of z central charges the largest semisimple part of the internal symmetry algebra is a direct sum of z compact symplectic group algebras and possibly an additional term representing the unimodular unitary group algebra. Next it is shown that 4j ? N + K, where j is the highest spin value of the underlying fields, N is the number of spinorial charges and K the number of these spinorial charges which are not linked to other spinorial charges by a central charge. It is further demonstrated that, in general, the central charge can not be redefined in such a way that it is at the same time real and preserves the locality principle. The discussion of the obtained results concludes the paper.     

Infinite symmetry algebras of extended supergravity theories

When extended supergravity theories with noncompact symmetry groups are written in a physical gauge, the noncompact symmetries join with the supersymmetries to generate an infinite-dimensional algebra. The details are worked out explicitly for a two-dimensional theory with an SU(1, 1) internal symmetry. Our analysis confirms the observation of Ellis et al. that the infinite rigid superalgebra should be obtained from the finite-dimensional local superalgebra by replacing scalar fields with their asymptotic values at infinity. The infinite algebra is described by extending the super-Poincaré generators to functions on the coset space defined by the scalar fields at infinity. While mathematically nontrivial, this result is, in a certain sense, trivial from a physical point of view.     

The soliton supermultiplet in 4 + 1 dimensions

We consider the SO(4) = SU(2) ? USp(2) Clifford algebra, obtained by the supersymmetry algebra for the N = 2 supersymmetric Yang-Mills theory in 4+1 dimensions, which, in the phase of unbroken gauge symmetry, has a topological charge as central charge. We find that, even if the Higgs mechanism is absent, the massive soliton supermultiplet contains the same number of states as the massless supermultiplet of elementary particles.     

Holography at an extremal De Sitter horizon

Rotating maximal black holes in four-dimensional de Sitter space, for which the outer event horizon coincides with the cosmological horizon, have an infinite near-horizon region described by the rotating Nariai metric. We show that the asymptotic symmetry group at the spacelike future boundary of the near-horizon region contains a Virasoro algebra with a real, positive central charge. This is evidence that quantum gravity in a rotating Nariai background is dual to a two-dimensional Euclidean conformal field theory. These results are related to the Kerr/CFT correspondence for extremal black holes, but have two key differences: one of the black hole event horizons has been traded for the cosmological horizon, and the near-horizon geometry is a fiber over dS₂ rather than AdS₂.     

Conservative Currents of Boundary Charges in AdS2 1 Gravity

The boundary charge which constitutes the Virasoro algebra in (2- 1)-dirnensional anti-de Sitter gravity is derived by Noether theorem and diffeomorphic invariance. It shows that the boundary charge under discussion recently exhausts all the available independent nontrivial charges. Therefore, for any specific spacetime, the state counting via the central charge of the Virasoro algebra is exact.``     

Conservative Currents of Boundary Charges in AdS2+1 Gravity

The boundary charge which constitutes the Virasoro algebra in (2+1)-dimensional anti-de Sitter gravity is derived by Noether theorem and diffeomorphic invariance. It shows that the boundary charge under discussion recently exhausts all the available independent nontrivial charges. Therefore, for any specific spacetime, the state counting via the central charge of the Virasoro algebra is exact.     

Asymptotic symmetry of geometries with Schrödinger isometry

We show that the asymptotic symmetry algebra of geometries with Schrödinger isometry in any dimension is an infinite-dimensional algebra containing one copy of Virasoro algebra. It is compatible with the fact that the corresponding geometries are dual to non-relativistic CFTs whose symmetry algebra is the Schrödinger algebra which admits an extension to an infinite-dimensional symmetry algebra containing a Virasoro subalgebra.     

Null-plane charges and fourier transforms for explicitly and spontaneously broken symmetries

It is shown that the existence of null-plane charges and null-plane Fourier transforms (which enter into the discussion of current algebra at infinite momentum) depends on the high energy asymptotic behaviour of off mass shell scattering amplitudes; s In s behaviour is the maximum growth allowed. Under the assumption that asymptotic states exist, these results also hold in the case of spontaneously broken chiral symmetry with massless pseudoscalar Goldstone bosons. In this case, the resulting charges are the non-conserved pole-free charges suggested by Carlitz et al.     

Statistical entropies of extremal Kaluza-Klein AdS black holes in arbitrary dimensions

We have investigated the microscopic interpretations of the entropies for the four-dimensional extremal Kaluza-Klein AdS black hole and its higher-dimensional generalizations by using the Kerr/CFT correspondence. These newly-found Kaluza-Klein AdS black holes are charged rotating asymptotically AdS black hole solutions of gauged supergravity in four and higher dimensions. With suitable boundary conditions on the perturbations of the near-horizon geometry, it is shown that the asymptotic symmetry generators form a two-dimensional Virasoro algebra with a central term. By utilizing the central charge and the temperature of the dual conformal field theory, Cardy formula reproduces the expected Bekenstein-Hawking entropy. Directly working on the ordinary metrics of the extremal Kaluza-klein AdS black holes without taking the near-horizon limit, we also re-derive their microscopic entropies.     

c-Theorem for disordered systems

We find an analog of Zamolodchikov's c-theorem for disordered two-dimensional non-interacting systems in their supersymmetric field theory representation. We show that the energy momentum tensor of such field theories must be a part of a supermultiplet, and that a new parameter b can be introduced with the help of that multiplet. b flows along the renormalization group trajectories much like the central charge for unitary two-dimensional field theories. While it has not been established if this flow is irreversible, that is, if b always flows down to lower values, it does so for all the cases worked out so far. b gives a new way to label different conformal field theories for disordered systems whose central charge is always 0. b turns out to be related to the central extension of a certain algebra, a generalization of the Virasoro algebra, which we show may be present at the critical points of these theories. b is also related to the finite size corrections of the physical free energy of disordered systems. We discuss possible applications by computing b for two-dimensional Dirac fermions with random gauge potential, in other words, for U(1∣1) Kac-Moody algebra.     

Scattering and infinite dimensional symmetry schemes

We examine the recently proposed non-trivial binding of the Poincare group with internal symmetry groups, which leads to mass splitting without symmetry breaking, from the point of view of scattering. We give a very general realization of the corresponding infinite dimensional Lie algebra in the Fok space of asymptotic states built from two scalar nucleons. Assuming that the algebra describes the exact symmetry of theS-matrix we conclude that no elastic NN scattering exists.The author is indebted to Professor V. Votruba and Dr. J. Formánek for many stimulating discussions.     

Enveloping algebra identities on solutions of conformally invariant wave equations

We study identities in the enveloping algebra of the conformal group, which is the symmetry group of many wave equations: d'Alambert, Weyl, Maxwell, etc. We find all second-order identities for these equations and, in addition, the dimension of the space of nontrivial symmetry operators of any order for the d'Alambert equation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 14–18, September, 1991.     

Local symmetries of massless wave equations

The structure of a wave-equation symmetry algebra for massless particles is studied. It is shown that the local-symmetry algebra of massless wave equations belongs to the enveloping algebra of a conformal-group Lie algebra. It is also proven that the space of nontrivial symmetries of fixed order is irreducible under adjoint representation of the conformal algebra, and its dimension is indicated. Omsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 19–26, May, 1998.     

All possible generators of supersymmetries of the S-matrix

A generator of a symmetry or supersymmetry of the S-matrix has to have three simple properties (see sect. 2). Starting from these properties one can give a complete analysis of the possible structure of the pseudo Lie algebra of these generators. In a theory with non-vanishing masses one finds that the only extension of previously known relations is the possible appearance of “central charges” as anticommutators of Fermi charges. In the massless case (disregarding infrared problems and symmetry breaking) the Fermi charges may generate the conformal group together with a unitary internal symmetry group.     

C-disorder fields and Γ(2)-invariant partition functions in parafermionic conformal field theories

The character formulae for the C-disorder fields corresponding to the charge conjugation symmetry in the parafermionic conformal field theories of Zamolodchikov and Fateev are obtained. These characters span a unitary representation of the level 2 subgroup Γ(2) of the full modular group. The corresponding Γ(2)-invariant partition functions are calculated. Derivation of the character formula is based on the relation between the parafermionic theories and the twisted N = 2 superconformal algebra. A similar idea is applied to explicitly construct the highest weight modules of the twisted SU(2) Kac-Moody algebra.     

Conformally invariant Yang-Mills theory realizing the Virasoro-Kac-Moody algebra

We will discuss a conformally invariant Yang-Mills theory in two dimensions, which realizes the Virasoro-Kac-Moody algebra as the BRST symmetry. The theory will have the Virasoro anomaly with the central charge −26, but no anomaly for the Kac-Moody algebra.     

Some general properties of representations of local currents

Some properties of representations of local current operators are studied. The currents are assumed to be conserved and to have charge densities transforming like the regular representation of any internal symmetry group G containing the isospin SU₂. The representation space is the “physical” Hilbert space, having a positive definite metric and carrying time-like positive-energy representations of the Poincaré group. The main results are that in every irreducible representation space, (A) arbitrarily large irreducible representations of G must occur, and (B) the mass spectrum is unbounded and continuous from some point onwards if it is not strictly degenerate. These results have strong implications for current algebra saturation schemes, both at finite and infinite momentum.     

Cosmology and the fate of dilatation symmetry

We discuss the cosmological constant problem in the light of dilatation symmetry and its possible anomaly. For dilatation symmetric quantum theories realistic asymptotic cosmology is obtained provided the effective potential has a nontrivial minimum. For theories with dilatation anomaly one needs as a nontrivial “cosmon condition” that the energy-momentum tensor in the vacuum is purely anomalous. Such a condition is related to the short distance renormalization group behaviour of the fundamental theory. Observable deviations from the standard hot big bang cosmology are possible.     

Light-cone quantisation and manifestation of non-perturbative vacuum properties for scalar field theory

For a quantum field theory with interacting scalar fields treated in light-cone quantisation (LCQ) it is shown that the vacuum of the theory is always the perturbative vacuum. The fields can be split up into classical constant fields, determined by minima of the effective action, and quantum fields. The former ones replace the nontrivial vacuum expectation values of the conventionally quantised theory. When spontaneous symmetry breaking occurs, the classical fields are only determined up to symmetry transformations. This degeneracy corresponds to the degeneracy of the vacuum in the conventional approach. The effective actions of the conventional theory and LCQ are identical. Lightcone charges obey the canonical commutation relations with the fields and the canonical charge algebra relations. Ward identities and the appearance of Goldstone Bosons accompanying spontaneous symmetry breaking can be derived in analogy to the conventional case.     

AdS2 supergravity and superconformal quantum mechanics

We investigate the asymptotic dynamics of topological anti-de Sitter supergravity in two dimensions. Starting from the formulation as a BF theory, it is shown that the AdS₂ boundary conditions imply that the asymptotic symmetries form a super-Virasoro algebra. Using the central charge of this algebra in Cardy’s formula, we exactly reproduce the thermodynamical entropy of AdS₂ black holes. Furthermore, we show that the dynamics of the dilaton and its superpartner reduces to that of superconformal transformations that leave invariant one chiral component of the stress tensor supercurrent of a two-dimensional conformal field theory. This dynamics is governed by a supersymmetric extension of the de Alfaro-Fubini-Furlan model of conformal quantum mechanics. Finally, two-dimensional de Sitter gravity is also considered, and the dS₂ entropy is computed by counting CFT states.