scholarly journals Ashtekar's variables for arbitrary gauge group

1992 ◽  
Vol 46 (6) ◽  
pp. R2279-R2282 ◽  
Author(s):  
Peter Peldán
Keyword(s):  
Gauge Group ◽  
Ashtekar's Variables ◽  
Arbitrary Gauge

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.

scholarly journals The SUSY Yang–Mills plasma in a T-matrix approach

2015 ◽  
Vol 30 (24) ◽  
pp. 1550145 ◽  
Author(s):  
Gwendolyn Lacroix ◽  
Claude Semay ◽  
Fabien Buisseret
Keyword(s):  
Gauge Group ◽  
Bound States ◽  
Bound State ◽  
Lattice Data ◽  
Superstring Theory ◽  
Matrix Formulation ◽  
Yang Mills ◽  
Bound State Spectrum ◽  
T Matrix ◽  
Arbitrary Gauge

In this paper, the thermodynamic properties of [Formula: see text] supersymmetric Yang–Mills theory with an arbitrary gauge group are investigated. In the confined range, we show that identifying the bound state spectrum with a Hagedorn one coming from noncritical closed superstring theory leads to a prediction for the value of the deconfining temperature [Formula: see text] that agrees with recent lattice data. The deconfined phase is studied by resorting to a [Formula: see text]-matrix formulation of statistical mechanics in which the medium under study is seen as a gas of quasigluons and quasigluinos interacting nonperturbatively. Emphasis is put on the temperature range (1–5) [Formula: see text], where the interactions are expected to be strong enough to generate bound states. Binary bound states of gluons and gluinos are indeed found to be bound up to 1.4 [Formula: see text] for any gauge group. The equation of state is then computed numerically for [Formula: see text] and [Formula: see text], and discussed in the case of an arbitrary gauge group. It is found to be nearly independent of the gauge group and very close to that of nonsupersymmetric Yang–Mills when normalized to the Stefan–Boltzmann pressure and expressed as a function of [Formula: see text].

scholarly journals GRAVITY AND YANG-MILLS THEORY: TWO FACES OF THE SAME THEORY?

1994 ◽  
Vol 03 (04) ◽  
pp. 695-722 ◽  
Author(s):  
SUBENOY CHAKRABORTY ◽  
PETER PELDÁN
Keyword(s):  
Phase Space ◽  
Gauge Group ◽  
Weak Field ◽  
De Sitter ◽  
Yang Mills ◽  
Sitter Spacetime ◽  
Lorentzian Signature ◽  
Spherically Symmetric Solution ◽  
Higgs Scalar ◽  
Arbitrary Gauge

We introduce a gauge and diffeomorphism invariant theory on the Yang-Mills phase space. The theory is well defined for an arbitrary gauge group with an invariant bilinear form, it contains only first class constraints, and the spacetime metric has a simple form in terms of the phase space variables. With gauge group SO (3, C), the theory equals the Ashtekar formulation of gravity with a cosmological constant. For Lorentzian signature, the theory is complex, and we have not found any good reality conditions. In the Euclidean signature case, everything is real. In a weak field expansion around de Sitter spacetime, the theory is shown to give the conventional Yang-Mills theory to the lowest order in the fields. We show that the coupling to a Higgs scalar is straightforward, while the naive spinor coupling does not work. We have not found any way of including spinors that gives a closed constraint algebra. For gauge group U(2), we find a static and spherically symmetric solution.

ANOMALY THROUGH GAUGE-INVARIANT REGULARIZATION WITH INFINITE NUMBER OF PAULI-VILLARS FIELDS

1993 ◽  
Vol 08 (37) ◽  
pp. 3517-3528 ◽  
Author(s):  
SINYA AOKI ◽  
YOSHIO KIKUKAWA
Keyword(s):  
Gauge Theory ◽  
Gauge Group ◽  
Infinite Number ◽  
Invariant Form ◽  
Chiral Fermion ◽  
Gauge Invariant ◽  
Invariant Regularization ◽  
Arbitrary Gauge

Abelian anomaly is examined by means of the recently proposed gauge-invariant regularization for SO(10) chiral gauge theory and its generalization for a theory of arbitrary gauge group with anomaly-free chiral fermion contents. For both cases it is shown that the anomaly with correct normalization can be obtained in a gauge-invariant form without any counterterms.

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