DOES HETEROTIC STRING GENERATE CHERN-SIMONS ACTION IN THREE DIMENSIONS?

1992 ◽  
Vol 07 (20) ◽  
pp. 1805-1815 ◽  
Author(s):  
HITOSHI NISHINO
Keyword(s):  
Field Strength ◽  
String Tension ◽  
Heterotic String ◽  
Three Dimensions ◽  
Simons Theory ◽  
Coupling Constant ◽  
Yang Mills ◽  
Close Relationship ◽  
Chern Simons ◽  
Chern Simons Theory

We study the possibility that the ten-dimensional (D=10) heterotic superstring generates a class of Chern-Simons theories in three dimensions, via compactifications on the internal seven-dimensional manifolds. We give an explicit example of such compactifications on (Calabi-Yau)6×S1×(Mink.)3, using the dual formulation of the heterotic string. The string tension 1/α′ as well as the Yang-Mills coupling constant g2 in D=10 is double-quantized in terms of two integers, through a condensate of the antisymmetric field strength NM1…M7, which is dual to the ordinary field strength GMNP. The resultant Chern-Simons theory has the gauge group E6⊗E8, containing also the usual kinetic terms of the gauge fields, which may be interpreted as regulator terms. This result suggests a close relationship between the D=10 heterotic string and D=3 Chern-Simons theory.

scholarly journals Yang-Mills theory, 2 + 1 and 3 + 1 dimensions

2003 ◽  
Vol 18 (33n35) ◽  
pp. 2415-2422 ◽  
Author(s):  
V. P. NAIR
Keyword(s):  
String Tension ◽  
Simons Theory ◽  
Nonzero Temperature ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Magnetic Mass ◽  
Chern Simons ◽  
Chern Simons Theory

I review the analysis of (2+1)-dimensional Yang-Mills (YM2+1) theory via the use of gauge-invariant matrix variables. The vacuum wavefunction, string tension, the propagator mass for gluons, its relation to the magnetic mass for YM3+1at nonzero temperature and the extension of our analysis to the Yang-Mills-Chern-Simons theory are discussed. A possible extension to 3 + 1 dimensions is also briefly considered.

D = 3 Gauge Dynamics: Yang-Mills and Yang-Mills-Chern-Simons Theory

1997 ◽  
Vol 12 (06) ◽  
pp. 1023-1031 ◽  
Author(s):  
John M. Cornwall
Keyword(s):  
Three Dimensions ◽  
Simons Theory ◽  
Dynamical Mass ◽  
Yang Mills ◽  
Quantum Vortex ◽  
Dynamical Generation ◽  
Perturbative Regime ◽  
Vortex Solitons ◽  
Chern Simons ◽  
Chern Simons Theory

We summarize recent progress in understanding non-perturbative effects of Yang-Mills (YM) and Yang-Mills Chern-Simons (YMCS) theories in three dimensions, based on a monopole-vortex vacuum condensate. In YM theory these include dynamical generation of a gluon mass, quantum vortex solitons, and and entropy-driven condensate of these solitons. This leads to confinement as well as CS fluctuations (related to B+L violation). These two phenomena are both described in terms of topological linkings of closed vortices with a Wilson loop (confinement) or with each other (CS fluctuations). In SU(N) YMCS theory with a level-k CS term, similar effects occur for k less than a critical value kc ≈ 2N, while for larger k there is a phase transition to a purely perturbative regime with no dynamical mass (just the perturbative CS mass), solitons, or condensate.

Infrared finiteness of the two-loop correction to the Chern–Simons term in the Yang–Mills–Chern–Simons theory

1995 ◽  
Vol 73 (5-6) ◽  
pp. 344-348 ◽  
Author(s):  
Yeong-Chuan Kao ◽  
Hsiang-Nan Li
Keyword(s):  
Effective Action ◽  
Background Field ◽  
Landau Gauge ◽  
Quantum Corrections ◽  
Simons Theory ◽  
Loop Correction ◽  
Loop Contribution ◽  
Yang Mills ◽  
Chern Simons ◽  
Chern Simons Theory

We show that the two-loop contribution to the coefficient of the Chern–Simons term in the effective action of the Yang–Mills–Chern–Simons theory is infrared finite in the background field Landau gauge. We also discuss the difficulties in verifying the conjecture, due to topological considerations, that there are no more quantum corrections to the Chern–Simons term other than the well-known one-loop shift of the coefficient.

scholarly journals BATALIN–VILKOVISKY YANG–MILLS THEORY AS A HOMOTOPY CHERN–SIMONS THEORY VIA STRING FIELD THEORY

2009 ◽  
Vol 24 (07) ◽  
pp. 1309-1331 ◽  
Author(s):  
ANTON M. ZEITLIN
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Simons Theory ◽  
Yang Mills ◽  
Algebraic Constructions ◽  
Chern Simons ◽  
Chern Simons Theory

We show explicitly how Batalin–Vilkovisky Yang–Mills action emerges as a homotopy generalization of Chern–Simons theory from the algebraic constructions arising from string field theory.

scholarly journals STATIC POTENTIAL AND A NEW GENERALIZED CONNECTION IN THREE DIMENSIONS

2004 ◽  
Vol 19 (22) ◽  
pp. 1695-1700 ◽  
Author(s):  
PATRICIO GAETE
Keyword(s):  
Gauge Theory ◽  
Three Dimensions ◽  
Simons Theory ◽  
Static Potential ◽  
Gauge Invariant ◽  
Confining Potential ◽  
Static Interaction ◽  
Pure Gauge Theory ◽  
Chern Simons ◽  
Chern Simons Theory

For a recently proposed pure gauge theory in three dimensions, without a Chern–Simons term, we calculate the static interaction potential within the structure of the gauge-invariant variables formalism. As a consequence, a confining potential is obtained. This result displays a marked qualitative departure from the usual Maxwell–Chern–Simons theory.

scholarly journals Averaging over Narain moduli space

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Alexander Maloney ◽  
Edward Witten
Keyword(s):  
Einstein Gravity ◽  
Two Dimensions ◽  
Three Dimensions ◽  
One Dimension ◽  
Simons Theory ◽  
Two Dimensional ◽  
Dual Theory ◽  
Recent Developments ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract Recent developments involving JT gravity in two dimensions indicate that under some conditions, a gravitational path integral is dual to an average over an ensemble of boundary theories, rather than to a specific boundary theory. For an example in one dimension more, one would like to compare a random ensemble of two-dimensional CFT’s to Einstein gravity in three dimensions. But this is difficult. For a simpler problem, here we average over Narain’s family of two-dimensional CFT’s obtained by toroidal compactification. These theories are believed to be the most general ones with their central charges and abelian current algebra symmetries, so averaging over them means picking a random CFT with those properties. The average can be computed using the Siegel-Weil formula of number theory and has some properties suggestive of a bulk dual theory that would be an exotic theory of gravity in three dimensions. The bulk dual theory would be more like U(1)2D Chern-Simons theory than like Einstein gravity.

scholarly journals $$ T\overline{T} $$-deformation of q-Yang-Mills theory

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Leonardo Santilli ◽  
Richard J. Szabo ◽  
Miguel Tierz
Keyword(s):  
Phase Transition ◽  
Entanglement Entropy ◽  
Simons Theory ◽  
Line Bundles ◽  
Boltzmann Entropy ◽  
Third Order ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We derive the $$ T\overline{T} $$ T T ¯ -perturbed version of two-dimensional q-deformed Yang-Mills theory on an arbitrary Riemann surface by coupling the unperturbed theory in the first order formalism to Jackiw-Teitelboim gravity. We show that the $$ T\overline{T} $$ T T ¯ -deformation results in a breakdown of the connection with a Chern-Simons theory on a Seifert manifold, and of the large N factorization into chiral and anti-chiral sectors. For the U(N) gauge theory on the sphere, we show that the large N phase transition persists, and that it is of third order and induced by instantons. The effect of the $$ T\overline{T} $$ T T ¯ -deformation is to decrease the critical value of the ’t Hooft coupling, and also to extend the class of line bundles for which the phase transition occurs. The same results are shown to hold for (q, t)-deformed Yang-Mills theory. We also explicitly evaluate the entanglement entropy in the large N limit of Yang-Mills theory, showing that the $$ T\overline{T} $$ T T ¯ -deformation decreases the contribution of the Boltzmann entropy.

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 .

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