1,721,023 research outputs found
REDUCED TENSOR ALGEBRA IN SU(3) CHERN-SIMONS FIELD THEORY
No full textWe consider the non-Abelian SU(3) Chern-Simons field theory defined in R3 and S3. The reconstruction theorems for the vacuum expectation values of the Wilson line operators are proved. We give in particular the general expressions for the values of the unknot and of the Hopf link. The physical consequences of the quantization of the coupling constant are studied in detail. The structure of the resulting reduced tensor algebra is derived
THE NONCOMMUTATIVE BRANE WORLD
No full textWe propose a new higher-dimensional mechanism to localize scalar fields as well as fermionic and gauge fields. The underlying theory is a six-dimensional non-commutative field theory where non-commutativity is allowed along two extra infinite spatial dimensions and the four-dimensional brane is provided by a scalar soliton living in the non-commutative space. Making use of the powerful correspondence between non-commutative coordinates and operators on a single particle Hilbert space, we show that the non-commutative brane world admits localized chiral fermions and it ensures the localization of massless gauge fields. It may also give rise to a variety of different low-energy spectra since the localized zero mode may come along either with a discrete tower of degenerate heavy states or with a tower of Kaluza-Klein heavy states, or it may even be the only state in the low-energy spectrum
SU(3) CHERN-SIMONS FIELD THEORY IN THREE MANIFOLDS
No full textWe present the solution of the non-Abelian SU (3) Chern-Simons field theory defined in a generic three-manifold which is closed, connected and orientable. The surgery rules, which permit us to solve the theory, are derived and several examples of vacuum expectation values of Wilson line operators are computed. The three-manifold invariant associated with the non-Abelian SU (3) Chern-Simons model is defined and its values are computed for various three-manifolds
Bigravity as a tool for massive gravity
No full textThe formulation of massive gravity as bigravity is discussed. We argue that bigravity is more than a tool to tackle massive deformation of gravity
THREE-DIMENSIONAL TOPOLOGY AND VERLINDE FORMULA
No full textWe study the properties of the gauge invariant observables of the three-dimensional Chem-Simons field theory; it is shown that the algebra structure determined by the observables is isomorphic with the fusion rules of two-dimensional conformal theories. In the colour state space of the link components, a projective representation of the modular group is defined. The relations satisfied by the S matrix of the conformal models admit an interpretation in terms of three-dimensional topology; we describe the topological origin of these relations
THREE MANIFOLD INVARIANTS AND THEIR RELATION WITH THE FUNDAMENTAL GROUP
No full textWe consider the 3-manifold invariant I(M) which is defined by means of the Chern-Simons quantum field theory and which coincides with the Reshetikhin-Turaev invariant. We present some arguments and numerical results supporting the conjecture that for nonvanishing I(M), the absolute value \I(M)\ only depends on the fundamental group pi(1)(M) of the manifold M. For lens spaces, the conjecture is proved when the gauge group is SU(2). In the case in which the gauge group is SU(3), we present numerical computations confirming the conjecture
LOCALIZATION OF QUANTUM FIELDS ON BRANES
No full textA mechanism for localization of quantum fields on a s-brane, representing the boundary of a (s + 2)-dimensional bulk space, is investigated. Minkowski and AdS bulk spaces are analyzed. Besides the background geometry, the relevant parameters controlling the theory are the mass M and a real parameter eta, specifying the boundary condition on the brane. The importance of exploring the whole range of allowed values for these parameters is emphasized. Stability in Minkowski space requires eta greater than or equal to -M, whereas in the AdS background all real eta are permitted. Both in the flat and in AdS case, the induced field on the brane is a non-canonical generalized free field. For a suitable choice of boundary condition, corresponding to the presence of a boundary state, the induced field on the brane mimics standard (s + 1)-dimensional physics. In a certain range of eta, the spectral function in the the AdS case is dominated by a massive excitation, which imitates the presence of massive particle on the brane. We show that the quantum field induced on the brane is stabl
ON ANOMALIES IN ORBIFOLD THEORIES
No full textWe study the issue of gauge invariance in five-dimensional theories compactified on an orbifold S1/(Z2 ×Z′2) in the presence of an external U(1) gauge field. From the four-dimensional point of view the theory contains a tower of Kaluza–Klein Dirac fermions with chiral couplings and it looks anomalous at the quantum level. We show that this “anomaly” is cancelled by a topological Chern–Simons term which is generated in the effective action when the gauge theory is regularized introducing a Pauli–Villars fermion with an odd mass term. In the presence of a classical background gauge field, the fermionic current acquires a vacuum expectation value, thus generating the suitable Chern–Simons term and a gauge invariant theory
BOSONIZATION AT FINITE TEMPERATURE AND ANYON CONDENSATION
No full textAn operator formalism for bosonization at finite temperature and density is developed. We treat the general case of anyon statistics. The exact n-point correlation functions, satisfying the Kubo-Martin-Schwinger condition, are explicitly constructed, The invariance under both vector and axial transformations allows to introduce two chemical potentials, which give rise to non-vanishing persistent currents. Investigating the exact momentum distribution, we discover anyon condensation in certain range of the statistical parameter, which shows that condensation is not an exclusive prerogative of bosonic systems. As an application of the general formalism, we solve the massless Thirring model at finite temperature, deriving the charge density and the persistent current
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