scholarly journals BOSE–FERMI EQUIVALENCE IN THREE-DIMENSIONAL NONCOMMUTATIVE SPACETIME

2008 ◽  
Vol 23 (35) ◽  
pp. 3015-3022
Author(s):  
K. M. AJITH ◽  
E. HARIKUMAR ◽  
M. SIVAKUMAR
Keyword(s):  
Partition Function ◽  
Gauge Field ◽  
Three Dimensional ◽  
Coupling Constant ◽  
Spin Factor ◽  
Noncommutative Spacetime ◽  
Chern Simons

We study the fermionisation of Seiberg–Witten mapped action (to order θ) of the λϕ4 theory coupled minimally with U(1) gauge field governed by Chern–Simons action. Starting from the corresponding partition function we derive nonperturbatively (in coupling constant) the partition function of the spin-1/2 theory following Polyakov spin factor formalism. We find that the dual interacting fermionic theory is nonlocal. This feature also persists in the limit of vanishing self-coupling. In θ → 0 limit, the commutative result is obtained.

scholarly journals ON THE UNIQUENESS OF D = 11 INTERACTIONS AMONG A GRAVITON, A MASSLESS GRAVITINO AND A THREE-FORM II: THREE-FORM AND GRAVITINI

2008 ◽  
Vol 23 (30) ◽  
pp. 4841-4859 ◽  
Author(s):  
EUGEN-MIHĂIŢĂ CIOROIANU ◽  
EUGEN DIACONU ◽  
SILVIU CONSTANTIN SĂRARU
Keyword(s):  
Master Equation ◽  
Gauge Field ◽  
Space Time ◽  
Free Solution ◽  
Coupling Constant ◽  
Abelian Gauge ◽  
Gauge Transformations ◽  
Lorentz Covariance ◽  
Brst Cohomology ◽  
Chern Simons

The interactions that can be introduced between a massless Rarita–Schwinger field and an Abelian three-form gauge field in 11 space–time dimensions are analyzed in the context of the deformation of the "free" solution of the master equation combined with local BRST cohomology. Under the hypotheses of smoothness of the interactions in the coupling constant, locality, Poincaré invariance, Lorentz covariance, and the presence of at most two derivatives in the Lagrangian of the interacting theory (the same number of derivatives as in the free Lagrangian), we prove that there are neither cross-couplings nor self-interactions for the gravitino in D = 11. The only possible term that can be added to the deformed solution to the master equation is nothing but a generalized Chern–Simons term for the three-form gauge field, which brings contributions to the deformed Lagrangian, but does not modify the original, Abelian gauge transformations.

scholarly journals PROBING THE FROISSART BOUND FOR MODELS WITH CHARGED VECTOR FIELDS IN D=3

1994 ◽  
Vol 09 (18) ◽  
pp. 1695-1700 ◽  
Author(s):  
O.M. DEL CIMA
Keyword(s):  
Asymptotic Behavior ◽  
Scattering Amplitudes ◽  
Gauge Field ◽  
Vector Fields ◽  
Three Dimensional ◽  
Tree Level ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Maxwell Fields ◽  
Chern Simons

One discusses the tree-level unitarity and presents asymptotic behavior of scattering amplitudes for three-dimensional gauge-invariant models where complex Chern- Simons-Maxwell fields (with and without a Proca-like mass) are coupled to an Abelian gauge field.

scholarly journals THE ζ FUNCTION ANSWER TO PARITY VIOLATION IN THREE-DIMENSIONAL GAUGE THEORIES

1996 ◽  
Vol 11 (15) ◽  
pp. 2643-2660 ◽  
Author(s):  
R.E. GAMBOA SARAVÍ ◽  
G.L. ROSSINI ◽  
F.A. SCHAPOSNIK
Keyword(s):  
Gauge Field ◽  
Parity Violation ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Mass Term ◽  
Three Dimensions ◽  
Fermion Mass ◽  
Chern Simons ◽  
Fermion Current ◽  
Arbitrary Gauge

We study parity violation in (2+1)-dimensional gauge theories coupled to massive fermions. Using the ζ function regularization approach we evaluate the ground state fermion current in an arbitrary gauge field background, showing that it gets two different contributions which violate parity invariance and induce a Chern–Simons term in the gauge field effective action. One is related to the well-known classical parity breaking produced by a fermion mass term in three dimensions; the other, already present for massless fermions, is related to peculiarities of gauge-invariant regularization in odd-dimensional spaces.

RENORMALIZATION AMBIGUITIES AND GAUGE SYMMETRY IN CHERN–SIMONS THEORIES

1998 ◽  
Vol 13 (07) ◽  
pp. 511-525
Author(s):  
J. L. LÓPEZ
Keyword(s):  
Effective Action ◽  
Three Dimensional ◽  
Gauge Coupling ◽  
Simons Theory ◽  
Radiative Corrections ◽  
Dirac Fermions ◽  
Coupling Constant ◽  
Effective Constant ◽  
Chern Simons ◽  
Chern Simons Theory

The universality of radiative corrections to the gauge coupling constant k of the Chern–Simons theory is studied in a very general regularization scheme in the background gauge formalism. The effective constant k eff induced by radiative corrections can be any real number depending on the balance between the ultraviolet behavior of scalar and pseudoscalar terms in the regularized action. This ambiguity of the effective action is related to the ambiguity in the parity anomaly of three-dimensional Dirac fermions. The effective action also contains a non-analytic term in the gauge field with the same coefficient and opposite gauge transformation in such a way that the effective action is gauge-invariant. The results open the possibility of a connection with non-rational two-dimensional conformal theories for non-integer values of k eff .

scholarly journals On partition functions of refined Chern-Simons theories on S3

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
M.Y. Avetisyan ◽  
R.L. Mkrtchyan
Keyword(s):  
Partition Function ◽  
Gauge Group ◽  
Topological Strings ◽  
Simons Theory ◽  
Partition Functions ◽  
Coupling Constant ◽  
Sine Functions ◽  
Chern Simons ◽  
Arbitrary Gauge ◽  
Chern Simons Theory

Abstract We present a new expression for the partition function of the refined Chern-Simons theory on S3 with an arbitrary gauge group, which is explicitly equal to 1 when the coupling constant is zero. Using this form of the partition function we show that the previously known Krefl-Schwarz representation of the partition function of the refined Chern-Simons theory on S3 can be generalized to all simply laced algebras.For all non-simply laced gauge algebras, we derive similar representations of that partition function, which makes it possible to transform it into a product of multiple sine functions aiming at the further establishment of duality with the refined topological strings.

DUALITY FOR ANYONS

1989 ◽  
Vol 04 (20) ◽  
pp. 1937-1943 ◽  
Author(s):  
T.H. HANSSON ◽  
A. KARLHEDE
Keyword(s):  
Gauge Field ◽  
Three Dimensional ◽  
Higgs Model ◽  
Duality Transformation ◽  
Abelian Higgs Model ◽  
Topological Excitations ◽  
Fractional Spin ◽  
Conserved Current ◽  
Chern Simons ◽  
Spin And Statistics

We study the Nielsen-Olesen vortices in the three dimensional noncompact Abelian Higgs model with a Chern-Simons term. The vortices are fractionally charged anyons (i.e., particles with fractional spin and statistics). In a certain limit we can express the theory in terms of these topological excitations by performing a duality transformation on the lattice. The result is a topologically conserved current describing the vortices, minimally coupled to a dynamical gauge field with a Chern-Simons term. Spin, statistics and size of the excitations are all preserved under this transformation.

GEOMETRIC REGULARIZATION AND GAUGE INVARIANCE IN CHERN–SIMONS THEORIES

1992 ◽  
Vol 07 (02) ◽  
pp. 235-256 ◽  
Author(s):  
MANUEL ASOREY ◽  
FERNANDO FALCETO
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Gauge Condition ◽  
Simons Theory ◽  
Coupling Constant ◽  
Gauge Transformations ◽  
Yang Mills ◽  
The One ◽  
Chern Simons ◽  
Three Dimensional Space

Some perturbative aspects of Chern–Simons theories are analyzed in a geometric-regularization framework. In particular, we show that the independence from the gauge condition of the regularized theory, which insures its global meaning, does impose a new constraint on the parameters of the regularization. The condition turns out to be the one that arises in pure or topologically massive Yang–Mills theories in three-dimensional space–times. One-loop calculations show the existence of nonvanishing finite renormalizations of gauge fields and coupling constant which preserve the topological meaning of Chern–Simons theory. The existence of a (finite) gauge-field renormalization at one-loop level is compensated by the renormalization of gauge transformations in such a way that the one-loop effective action remains gauge-invariant with respect to renormalized gauge transformations. The independence of both renormalizations from the space–time volume indicates the topological nature of the theory.

scholarly journals Gravitational dual of averaged free CFT’s over the Narain lattice

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Alfredo Pérez ◽  
Ricardo Troncoso
Keyword(s):  
Partition Function ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Simons Theory ◽  
Energy Tensor ◽  
The Family ◽  
Stress Energy ◽  
Higher Spin ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract It has been recently argued that the averaging of free CFT’s over the Narain lattice can be holographically described through a Chern-Simons theory for U (1)D×U (1)D with a precise prescription to sum over three-dimensional handlebodies. We show that a gravitational dual of these averaged CFT’s would be provided by Einstein gravity on AdS3 with U (1)D−1× U (1)D−1 gauge fields, endowed with a precise set of boundary conditions closely related to the “soft hairy” ones. Gravitational excitations then go along diagonal SL (2, ℝ) generators, so that the asymptotic symmetries are spanned by U (1)D× U (1)D currents. The stress-energy tensor can then be geometrically seen as composite of these currents through a twisted Sugawara construction. Our boundary conditions are such that for the reduced phase space, there is a one-to-one map between the configurations in the gravitational and the purely abelian theories. The partition function in the bulk could then also be performed either from a non-abelian Chern-Simons theory for two copies of SL (2, ℝ) × U (1)D−1 generators, or formally through a path integral along the family of allowed configurations for the metric. The new boundary conditions naturally accommodate BTZ black holes, and the microscopic number of states then appears to be manifestly positive and suitably accounted for from the partition function in the bulk. The inclusion of higher spin currents through an extended twisted Sugawara construction in the context of higher spin gravity is also briefly addressed.

scholarly journals RATIONAL CONFORMAL FIELD THEORY AND MULTIWORMHOLE PARTITION FUNCTION IN THREE-DIMENSIONAL GRAVITY

1993 ◽  
Vol 08 (22) ◽  
pp. 3909-3932 ◽  
Author(s):  
SHUN’YA MIZOGUCHI
Keyword(s):  
Partition Function ◽  
Initial Data ◽  
Three Dimensional ◽  
Lens Space ◽  
Conformal Field Theories ◽  
Positive Cosmological Constant ◽  
Modular Invariant ◽  
Conformal Field ◽  
Dimensional Gravity ◽  
Chern Simons

We study the Turaev-Viro (TV) invariant as the Euclidean Chern-Simons-Witten gravity partition function with positive cosmological constant. After explaining why it can be identified as the partition function of three-dimensional gravity, we show that the initial data of the TV invariant can be constructed from the duality data of a certain class of rational conformal field theories, and that, in particular, the original TV initial data are associated with the Ak+1 modular invariant SU(2) WZW model. As a corollary we then show that the partition function Z(M) is bounded from above by [Formula: see text], where g is the smallest genus of handlebodies with which M can be presented by Hegaard splitting. Z(M) is generically very large near Λ~+0 if M is neither S3 nor a lens space, and many-wormhole configurations dominate near Λ~+0 in the sense that Z(M) generically tends to diverge faster as the “number of wormholes” g becomes larger.

scholarly journals A nonperturbative method for the Yang–Mills Lagrangian

2015 ◽  
Vol 30 (13) ◽  
pp. 1550070 ◽  
Author(s):  
Renata Jora
Keyword(s):  
Partition Function ◽  
Gauge Field ◽  
Beta Function ◽  
Gauge Coupling ◽  
Field Method ◽  
Coupling Constant ◽  
Yang Mills ◽  
Nonperturbative Method ◽  
Renormalization Constants ◽  
Gauge Coupling Constant

Using the properties of the partition function for a Yang–Mills theory we compute simple relations among the renormalization constants. In the particular case of the background gauge field method we obtain that the all orders beta function for the gauge coupling constant contains only the first two orders coefficients different than zero and thus corresponds to the 't Hooft scheme.

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