3,095 research outputs found
ZETA-FUNCTION CALCULATION OF THE WEYL DETERMINANT FOR 2-DIMENSIONAL NON-ABELIAN GAUGE-THEORIES IN A CURVED BACKGROUND AND ITS W-Z-W TERMS
No full textUsing a cohomological characterization of the consistent and the covariant Lorentz and gauge anomalies, derived from the complexification of the relevant algebras, we study, in d = 2, the definition of the Weyl determinant for a non-Abelian theory with Riemannian background. We obtain two second-order operators that produce, by means of zeta-function regularization, respectively, the consistent and the covariant Lorentz and gauge anomalies, preserving diffeomorphism invariance. We compute exactly their functional determinants and the W-Z-W terms: the 'consistent' determinant agrees with the non-Abelian generalization of the classical Leutwyler's result, while the 'covariant' one gives rise to a covariant version of the usual Wess-Zumino-Witten action
COVARIANT ANOMALIES AND FUNCTIONAL DETERMINANTS
No full textWe analize the algebraic structure of consistent and covariant anomalies in gauge and gravitational theories: using a complex extension of the Lie algebra it is possible to describe them in a unified way. Then we study their representations by means of functional determinants, showing how the algebraic solution determines the relevant operators for the definition of the effective action. Particular attention is devoted to the Lorentz anomaly: we obtain by functional methods the covariant anomaly for the spin-current and for the energy-momentum tensor in presence of a curved background. With regard to the consistent sector we are able to give a general functional solution only for d = 2: using the characterization derived from the extended algebra, we find a continuous family of operators whose determinant describes the effective action of chiral spinors in curved space. We compute this action and we generalize the result in presence of a U(1) gauge connection
The instanton contributions to Yang-Mills theory on the torus: Localization, Wilson loops and the perturbative expansion
No full textCHIRAL ANOMALIES FOR VORTEX POTENTIALS IN 2 DIMENSIONS AND A DECOMPACTIFICATION LIMIT
No full textA complete set of eigenfunctions on a two-dimensional sphere is obtained for the Dirac operator corresponding to a vortexlike Abelian potential. Then a decompactification limit is studied from the sphere to R2, in which the potential leads to a constant field configuration. The chiral anomaly is studied by using first-order perturbation theory and the crucial role played by zero modes in this context is carefully discussed
Ghost decoupling in the 't Hooft spectrum for mesons
No full textWe show that the replacement of the ''instantaneous'' 't Hooft potential with the causal form suggested by equal time canonical quantization in the light-cone gauge, which entails the occurrence of negative probability states, does not change the bound state spectrum when the difference is treated as a single insertion in the kernel
Partition functions of chiral gauge theories on the two dimensional torus and their duality properties
No full textTwo different families of abelian chiral gauge theories on the torus are investigated: the aim is to test the consistency of two-dimensional anomalous gauge theories in the presence of global degrees of freedom for the gauge field. An explicit computation of the partition functions shows that unitarity is recovered in particular regions of parameter space and that the effective dynamics is described in terms of fermionic interacting models. For the first family, this connection with fermionic models uncovers an exact duality which is conjectured to hold in the nonabelian case as well
The quantum 1/2 BPS Wilson loop in N= 4 Chern-Simons-matter theories
No full textIn three dimensional N= 4 Chern-Simons-matter theories two independent fermionic Wilson loop operators can be defined, which preserve half of the supersymmetry charges and are cohomologically equivalent at classical level. We compute their three-loop expectation value in a convenient color sector and prove that the degeneracy is uplifted by quantum corrections. We expand the matrix model prediction in the same regime and by comparison we conclude that the quantum 1/2 BPS Wilson loop is the average of the two operators. We provide an all-loop argument to support this claim at any order. As a by-product, we identify the localization result at three loops as a correction to the framing factor induced by matter interactions. Finally, we comment on the quantum properties of the non-1/2 BPS Wilson loop operator defined as the difference of the two fermionic ones.Fil: Bianchi, Marco S.. Queen Mary, University Of London; Reino UnidoFil: Griguolo, Luca. Università di Parma; ItaliaFil: Leoni Olivera, Matías. Universidad de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Ecología, Genética y Evolución. Buenos Aires; ArgentinaFil: Mauri, Andrea. Universita Degli Studi Di Milano - Bicocca; ItaliaFil: Penati, Silvia. Universita Degli Studi Di Milano - Bicocca; Italia. Istituto Nazionale Di Fisica Nucleare, Frascati; ItaliaFil: Seminara, Domenico. Università degli Studi di Firenze; Itali
THE GENERALIZED CHIRAL SCHWINGER MODEL ON THE 2-SPHERE
No full textA family of theories which interpolate between vector and chiral Schwinger models is studied on the two-sphere S2. The conflict between the loss of gauge invariance and global geometrical properties is solved by introducing a fixed background connection. In this way the generalized Dirac-Weyl operator can be globally defined on S2. The generating functional of the Green functions is obtained by taking carefully into account the contribution of gauge fields with non-trivial topological charge and of the related zero-modes of the Dirac determinant. In the decompactification limit, the Green functions of the flat case are recovered; in particular the fermionic condensate in the vacuum vanishes, at variance with its behaviour in the vector Schwinger model
Classical solutions of the TEK model and noncommutative instantons in two dimensions
No full textThe twisted Eguchi-Kawai (TEK) model provides a non-perturbative de ̄nition
of noncommutative Yang-Mills theory: the continuum limit is approached at large-N by
performing suitable double scaling limits, in which non-planar contributions are no longer
suppressed. We consider here the two-dimensional case, trying to recover within this frame-
work the exact results recently obtained by means of Morita equivalence. We present a
rather explicit construction of classical gauge theories on noncommutative toroidal lattice
for general topological charges. After discussing the limiting procedures to recover the
theory on the noncommutative torus and on the noncommutative plane, we focus our at-
tention on the classical solutions of the related TEK models. We solve the equations of
motion and we ̄nd the con ̄gurations having ̄nite action in the relevant double scaling
limits. They can be explicitly described in terms of twist-eaters and they exactly cor-
respond to the instanton solutions that are seen to dominate the partition function on
the noncommutative torus. Fluxons on the noncommutative plane are recovered as well.
We also discuss how the highly non-trivial structure of the exact partition function can
emerge from a direct matrix model computation. The quantum consistency of the TEK
formulation is eventually checked by computing Wilson loops in a particular limit
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