Canonical quantization of spontaneously broken topologically. Dimensional topologically massive 2form gauge theory. There are also massive, charged excitations in this phase that come from the field. They illustrate how abelian gauge bosons may be attributed a physical mass without. Topologically massive gauge theories from first order. Gilkey and hanson, gravitation, gauge theories and differentialgeometry 1. The topologically massive gauge theories tmgt introduced in1, 2, 3 and their lowenergylimitthechernsimonscs theories are widely popular now, because of the possible applications for some condensed matter problems such as the fractional quantum hall effect fqhe4 and may be the high tc. Pdf onset of dynamical chaos in topologically massive. Benini alberto za aroni milanobicocca a topologically twisted index for three dimensional gauge theoriesstrings 2015 1. Moreover, the nonabelian extension of such kind of analysis has also been developed in. The gauge field lagrangian gauge invariant lagrangians for spin0 and sping. He argued that there is a monopole solution that is regular everywhere, but found that it does not possess finite action. Gauge theories and the standard model welcome to scipp. They are interesting because of their peculiar dynamical structure as well as for their connection to the hightemperature limit of fourdimensional theories 4.
On the origins of gauge theory university of toronto. This is done by explicitly realizing the quantum algebra on. We show that minimal massive 3d gravity mmg of 1, as well as the topological massive gravity, are particular cases of a more general minimal massive gravity theory with a single massive propagating mode arising upon spontaneous breaking of a local symmetry in a chernsimons gravity based on a hietarinta or maxwell algebra. First we discuss the connection of the topologically massive abelian gauge theory with contact geometry. A topologically twisted index for three dimensional gauge. In section 2, i introduce the basic kinematical and dynamical features of planar eld theories, such as anyons, topologically massive gauge elds and planar fermions.
Chernsimons gauge theories can be obtained by performing an inonuwigner. Quantum states of topologically massive electrodynamics. Pashaev joint institute for nuclear research, dubna, moscow 141980, russian federation and g. Onset of dynamical chaos in topologically massive gauge theories. This defect of procas model can be repaired either by stueckelbergs trick or by use of the higgs mechanism of mass generation which is essentially the same thing as our treatment of the gl functional. Gauge theories by way of introduction to the main text, let us give a brief survey of how mathematicians and physicists noticed and began to work on certain problems of mutual interest. Simon mass term have been studied by pisarski some years ago. This dual description has been extended to topologically massive gauge theories tmgt in any dimension.
But now the global topological symmetry u1top is unbroken. In an abelian topologically massive gauge theory, any eigenstate of the. In theoretical physics, massive gravity is a theory of gravity that modifies general relativity by endowing the graviton with a nonzero mass. In the vector case, the massless maxwell excitation, which is spinless, becomes massive with spin 1. Duality between topologically massive and selfdual models. Aspects of screening and confinement in a topologically. Pdf we study topologically massive b \wedge f abelian and nonabelian gauge theories in four dimensions, and reduce them to three.
Index theorems for the classical elliptic complexes 350 5,3. This formalism, applicable to yangmills theories as well as to gravity, not only provides us a transparent understanding in the scattering theoretical aspects, but also makes it possible to discuss other important problems directly. There were no exact or numerical solutions being presented by him. Classical and semiclassical techniques, other special classical field theories, unified field theories and models, lagrangian and hamiltonian approach.
Dissipation and topologically massive gauge theories. In particular, in the method of integrating one or the other gauge field in models with maxwell and chernsimons terms has been employed to establish the duality between topologically massive and selfdual gauge theories first discussed in. Section 4 deals with the derivation of the proper offshell nilpotent and absolutely anticommuting antibrst symmetry transformations of the yangmills. Dissipation and topologically massive gauge theories in the pseudoeuclidean plane m. Topological gravity as large n topological gauge theory. On topologically massive spin2 gauge theories beyond three. In the limit of strong fields, slowly varying in space spatially homogeneous fields, this theory is an analog. We propose here the maxwellbf model as a new kind of topological theory in four spacetime.
Topologically massive gauge theories inspire inspire hep. It is a driving concept to unify these forces into a single, comprehensive theory. Center for theoretical physics, laboratory for nuclear science and department of physics, massachusetts institute of technology, cambridge, massachusetts 02is9 received 22 january 1982 threedimensional yangmills and gravity theories augmented by gaugeinvariant mass terms are analyzed. Gravitation, gauge theories and differential geometry 215 5. Background solutions of topologically gauged cfts with 8 supersymmetries in preparation. Regularization scheme ambiguities in topologically massive. We therefore introduce a gauge invariant factorization of the classical phase space in two. The deformed dispersion relations induced by noncommutativity are derived and their implications on the quantum consistency of the theory are discussed. It is shown that in both theories the states are described by infraredregular polarization tensors containing a regularization phase which depends on the spin. We investigate the perturbative dynamics of noncommutative topologically massive gauge theories with softly broken supersymmetry. We show that, with the help of a general brst symmetry, different theories in 3 dimensions can be connected through a fundamental topological field theory related to the classical limit of the chernsimons model. We obtain a lorentzian solution for the topologically massive non abelian gauge theory on ads space by means of a su1, 1 gauge. Gauge vector and gravity models are studied in threedimensional spacetime, where novel, gauge invariant, p and t odd terms of topological.
Topologically massive gravity and gauge theory are dynamical theories which are speci. Aspects of chernsimons theory cern document server. In this paper we investigate the canonical quantization of a non. The symmetry group g can be expressed in general as a direct product of a. A topologically twisted index for three dimensional gauge theories alberto za aroni universit a di milanobicocca strings 2015, bangalore work in collaboration with f. When interacting with fermions, the quantum theory is infrared and ultraviolet finite in perturbation theory. They provide an alternative way to introduce mass term with no spontaneous symmetry breaking. Volume 281, issues 12, 10 april 2000, pages 409449. Theories of the fundamental interactions uclouvain. Pdf topologically massive nonabelian gauge theories. Such a model produces the chernsimonshiggs mechanism in which the gauge excitations acquire mass both from. Threedimensional massive gauge theories caltech authors.
In fact, 3d general relativity is a special case of one of the most important topological gauge theories for our purposesa theory called bftheoryso we begin with a description of that. Gauge vector and gravity models are studied in threedimensional spacetime, where novel, gauge invariant, p and t odd terms of topological origin give rise to masses for the gauge fields. Chernsimons states and topologically massive gauge theories. Threedimensional yangmills and gravity theories augmentedby gauge invariant mass terms are analyzed. Gauge invariant factorisation and canonical quantisation of topologically massive gauge theories in any dimension bruno bertrand and jan govaerts, july 6, 2006 refereed paper. Polysymplectic formulation for topologically massive yang. Gauge vector and gravity models are studied in threedimensional spacetime, where novel, gauge invariant, p and t odd terms of topological origin give rise to. The apparent clash between gauge symmetry and massive gauge bosons is avoided in the framework of topologically massive gauge theories, as it is the case for the wellknown maxwellchernsimons 1 and cremmerscherkkalbramondmodels cskr 25. This letter introduces an unconventional approach to the construction of this type of duality through a. Topologically protected duality on the boundary of maxwell. These topologically nontrivial additions profoundly alter the particle content of the models and lead to quantization of a dimensionless mass couplingconstant ratio. We found that the lagrangian for the massive proca fields is not gaugeinvariant. Topologically massive gauge theories in threedimensional spacetime have been exten sively studied in the past few years l81. Topologically massive gauge theories caltechauthors.
Static potential in a topologically massive borninfeld. The deformed dispersion relations induced by noncommutativity are derived and their implications on the quantum consistency of. This is done by explicitly realizing the quantum algebra on a functional hilbert space and by finding the. Nilsson chalmers university of technology, gothenburg talk at miami 2012 fort lauderdale december 14, 2012 talk based on. Benini alberto za aroni milanobicocca a topologically twisted index for three dimensional gauge theoriesstrings 2015 1 26. Pdf dissipation and topologically massive gauge theories. Dissipation and topologically massive gauge theories in. Topological gauge theory, and gravity derek keith wise.
In this way, we can extract a computable, yet highly nontrivial piece out of string theory and see if it has a large n description in the spirit of the matrix approach. Topologically massive gauge theories and the forcefree. On the origins of gauge theory callum quigley april 14, 2003 1 introduction we know the universe to be governed by four fundamental interactions. Pdf spontaneously broken 3d hietarintamaxwell chern. For any integer n 2 we introduce a conformal spin\\. In the classical theory, this means that gravitational waves obey a massive wave equation and hence travel at speeds below the speed of light massive gravity has a long and winding history, dating back to the 1930s when wolfgang pauli. Such a model produces the chernsimonshiggs mechanism in which the gauge. The most distinctive feature of the topologically massive gauge theories. This dual description may be extended to topologically massive gauge theories tmgt for forms of arbitrary rank and in any dimension. Pdf dissipation and topologically massive gauge theories in. Research article aspects of screening and confinement in a. Abelian topologically massive chernsimons theory in which the gauge fields are minimally coupled to a multiplet of scalar fields in such a way that the gauge symmetry is spontaneously broken. Monopole solutions in topologically massive gauge theory. The analogy between the landau problem of a charged particle in a magnclic field and quantization of this gauge theory is considered, as well as the quantiziulon condition for the abelian chernsimons term.
Threedimensional yangmills and gravity theories augmented by gaugeinvariant mass terms are analyzed. Local covariant operator formalism of nonabelian gauge. The question also arises in what sense a topological theory with a maxwell coupling is still topological. The prototype model for su 2 u1 electroweak interactions. Topologically protected duality on the boundary of maxwellbf. Within the hamiltonian formulation, the embedded topological field theory tft is not made manifest.
Topologically massive gauge theories and their dual. Jul 20, 2010 monopoles in topologically massive su2 yang. Our work is organized according to the following out. When interacting with fermions, the quantum theory is infrared and ultraviolet finite in. Templeton, topologically massive gauge theories, annals phys. Finally, in section 5 we discuss the possibility of inducing a dynamical dilaton eld on the worldsheet and its potential relevance to the dynamics of mtheory. New insights into abelian topologically massive gauge theories. On topologically massive spin2 gauge theories beyond. Topologically massive gauge theories are dynamical theories which are speci. The different ntmgts studied are stuckelberg formulation of a a firstorder formulation involving one and twoform fields, b proca theory, and c massive. Hamiltonian analysis of linearised topologically massive gravity. Pdf we elaborate on conformal higherspin gauge theory in threedimensional 3d curved space. We analyze the equivalence between topologically massive gauge theory tmgt and different formulations of nontopologically massive gauge theories ntmgts in the canonical approach.
We found that the lagrangian for the massive proca fields is not gauge invariant. Chernsimons invariants and secondary characteristic 5. This communication introduces the construction of this type of duality through a reparametrization of the master theory action. I also discuss the discrete symmetries p, cand t, and nonabelian chernsimons gauge theories. Hamiltonian analysis of linearised topologically massive. New results in topologically gauged m2brane theories with 8 supersymmetries bengt e. For nonabelian models, topological considerations lead to a quantization condition on the dimensionless coupling constantmass ratio. The vector fiem excitations become massive, with spin 1 rather than. Induced dilaton in topologically massive quantum field theory. They are interesting because of their peculiar dynamical structure as well as for their connection to the hightemperature limit of.
Graziano dipartimento di fisica, universita di salerno, 84100 salerno, italy and infn gruppo collegato salerno o. We study the relationship between three nonabelian topologically massive gauge theories, viz. New results in topologically gauged m2brane theories. Hamiltonian can be decomposed into a factor describing massive propa gating gauge. Bertrand, bruno ucl eng abelian topologically massive gauge theories tmgt provide a topological mechanism to generate mass for any ptensor boson in any dimension. A manifestly covariant and local canonical operator formalism of nonabelian gauge theories is presented in its full detail. Dissipation and topologically massive gauge theories in the. Dissipation and topologically massive gauge theories in the pseudoeuclidean plane. The topologically massive gauge theories tmgt introduced in1, 2, 3 and their lowenergylimitthechernsimonscs theories are widely popular now, because of the possible applications for some condensed matter problems such as the fractional.
Our results further contribute to discussions of these structures. Topologically massive gauge theories sciencedirect. The result is equivalent to that of qed3 with a thirring interaction term among fermions, in the short distance regime. Noncommutative topologically massive gauge theory surrey. Pdf dimensional reduction of fourdimensional topologically. Pdf topologically massive higher spin gauge theories. The purpose of these lectures is to give an introduction to gauge theories and the standard 14.
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