The Condensate for SU(2) Gauge Theory in 1 + 1 Dimensions  Coupled to Massless Adjoint Fermions

We consider SU(2) Yang-Mills theory in 1+1 dimensions coupled to massless adjoint fermions. With all fields in the adjoint represention the gauge group is actually SU(2)/Z2, which possesses nontrivial topology. In particular, there are two distinct topological sectors and the physical vacuum state has a structure analogous to a θ vacuum. We show how this feature is realized in light-front quantization, using discretization of x- as an infrared regulator. We find exact expressions for the vacuum states and construct the analog of the θ vacuum. We calculate the bilinear condensate of the model. We argue that this condensate does not effect the spectrum of the massless theory but gives the string tenson of the massive theory.

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Self-dual propagating wave solutions in Yang-Mills gauge theory

Physical Review D ◽

10.1103/physrevd.19.3649 ◽

1979 ◽

Vol 19 (12) ◽

pp. 3649-3652 ◽

Cited By ~ 8

Author(s):

Eve Kovacs ◽

Shui-Yin Lo

Keyword(s):

Gauge Theory ◽

Yang Mills ◽

Wave Solutions

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Non-Abelian variation on the Savvidy vacuum of the Yang-Mills gauge theory

Physical Review D ◽

10.1103/physrevd.49.6849 ◽

1994 ◽

Vol 49 (12) ◽

pp. 6849-6856 ◽

Cited By ~ 7

Author(s):

Suzhou Huang ◽

A. R. Levi

Keyword(s):

Gauge Theory ◽

Yang Mills

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A CHERN–SIMONS E8 GAUGE THEORY OF GRAVITY IN D = 15, GRAND UNIFICATION AND GENERALIZED GRAVITY IN CLIFFORD SPACES

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887807002545 ◽

2007 ◽

Vol 04 (08) ◽

pp. 1239-1257 ◽

Cited By ~ 13

Author(s):

CARLOS CASTRO

Keyword(s):

Gauge Theory ◽

Grand Unification ◽

De Sitter ◽

Sitter Group ◽

Yang Mills ◽

Theory Of Gravity ◽

M Theory ◽

Chern Simons ◽

Topological Part ◽

Gauge Theory Of Gravity

A novel Chern–Simons E8 gauge theory of gravity in D = 15 based on an octicE8 invariant expression in D = 16 (recently constructed by Cederwall and Palmkvist) is developed. A grand unification model of gravity with the other forces is very plausible within the framework of a supersymmetric extension (to incorporate spacetime fermions) of this Chern–Simons E8 gauge theory. We review the construction showing why the ordinary 11D Chern–Simons gravity theory (based on the Anti de Sitter group) can be embedded into a Clifford-algebra valued gauge theory and that an E8 Yang–Mills field theory is a small sector of a Clifford (16) algebra gauge theory. An E8 gauge bundle formulation was instrumental in understanding the topological part of the 11-dim M-theory partition function. The nature of this 11-dim E8 gauge theory remains unknown. We hope that the Chern–Simons E8 gauge theory of gravity in D = 15 advanced in this work may shed some light into solving this problem after a dimensional reduction.

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Evidence for weak-coupling holography from the gauge/gravity correspondence for Dp-branes

Progress of Theoretical and Experimental Physics ◽

10.1093/ptep/ptz167 ◽

2020 ◽

Vol 2020 (2) ◽

Author(s):

Yasuhiro Sekino

Keyword(s):

Gauge Theory ◽

Free Field ◽

Scalar Fields ◽

Superstring Theory ◽

Spatial Direction ◽

Strongly Coupled ◽

Yang Mills ◽

Hooft Coupling ◽

Brane Solution ◽

Gauge Gravity

Abstract Gauge/gravity correspondence is regarded as a powerful tool for the study of strongly coupled quantum systems, but its proof is not available. An unresolved issue that should be closely related to the proof is what kind of correspondence exists, if any, when gauge theory is weakly coupled. We report progress about this limit for the case associated with D$p$-branes ($0\le p\le 4$), namely, the duality between the $(p+1)$D maximally supersymmetric Yang–Mills theory and superstring theory on the near-horizon limit of the D$p$-brane solution. It has been suggested by supergravity analysis that the two-point functions of certain operators in gauge theory obey a power law with the power different from the free-field value for $p\neq 3$. In this work, we show for the first time that the free-field result can be reproduced by superstring theory on the strongly curved background. The operator that we consider is of the form ${\rm Tr}(Z^J)$, where $Z$ is a complex combination of two scalar fields. We assume that the corresponding string has the worldsheet spatial direction discretized into $J$ bits, and use the fact that these bits become non-interacting when ’t Hooft coupling is zero.

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HIGHER GAUGE THEORY AND GRAVITY IN 2+1 DIMENSIONS

International Journal of Modern Physics A ◽

10.1142/s0217751x07037330 ◽

2007 ◽

Vol 22 (28) ◽

pp. 5155-5172 ◽

Cited By ~ 1

Author(s):

R. B. MANN ◽

E. M. POPESCU

Keyword(s):

Gauge Theory ◽

Two Dimensional ◽

Yang Mills ◽

Higher Dimensional ◽

Present Context ◽

Dimensional Gravity ◽

Wide Perspective ◽

Higher Gauge Theory ◽

Matter Fields ◽

New Framework

Non-Abelian higher gauge theory has recently emerged as a generalization of standard gauge theory to higher-dimensional (two-dimensional in the present context) connection forms, and as such, it has been successfully applied to the non-Abelian generalizations of the Yang–Mills theory and 2-form electrodynamics. (2+1)-dimensional gravity, on the other hand, has been a fertile testing ground for many concepts related to classical and quantum gravity, and it is therefore only natural to investigate whether we can find an application of higher gauge theory in this latter context. In the present paper we investigate the possibility of applying the formalism of higher gauge theory to gravity in 2+1 dimensions, and we show that a nontrivial model of (2+1)-dimensional gravity coupled to scalar and tensorial matter fields — the ΣΦEA model — can be formulated as a higher gauge theory (as well as a standard gauge theory). Since the model has a very rich structure — it admits as solutions black-hole BTZ-like geometries, particle-like geometries as well as Robertson–Friedman–Walker cosmological-like expanding geometries — this opens a wide perspective for higher gauge theory to be tested and understood in a relevant gravitational context. Additionally, it offers the possibility of studying gravity in 2+1 dimensions coupled to matter in an entirely new framework.

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SPECTRUM OF SCREENING MASSES FOR SU(2) GAUGE THEORY: UNIVERSALITY CLASS

International Journal of Modern Physics D ◽

10.1142/s0218271810017755 ◽

2010 ◽

Vol 19 (08n10) ◽

pp. 1725-1729

Author(s):

R. S. COSTA ◽

S. B. DUARTE ◽

M. CHIAPPARINI ◽

T. MENDES

Keyword(s):

Phase Transition ◽

Monte Carlo ◽

Gauge Theory ◽

Critical Temperature ◽

Variational Method ◽

Excited States ◽

Universality Class ◽

Yang Mills ◽

Exponential Method ◽

Deconfinement Phase Transition

In this work we study the spectrum of the lowest screening masses for Yang–Mills theories on the lattice. We used the SU(2) gauge group in (3 + 1) dmensions. We adopted the multiple exponential method and the so-called "variational" method, in order to detect possible excited states. The calculations were done near the critical temperature of the confinement-deconfinement phase transition. We obtained values for the ratios of the screening masses consistent with predictions from universality arguments. A Monte Carlo evolution of the screening masses in the gauge theory confirms the validity of the predictions.

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The θ-vacuum in SU(2) lattice gauge theory

Nuclear Physics B ◽

10.1016/0550-3213(88)90120-4 ◽

1988 ◽

Vol 305 (4) ◽

pp. 661-674 ◽

Cited By ~ 7

Author(s):

A.S. Kronfeld ◽

M.L. Laursen ◽

G. Schierholz ◽

C. Schleiermacher ◽

U.-J. Wiese

Keyword(s):

Gauge Theory ◽

Lattice Gauge Theory ◽

Lattice Gauge ◽

Θ Vacuum

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Superfield approach to nilpotent symmetries in 3D Jackiw–Pi model of massive non-Abelian theory

Canadian Journal of Physics ◽

10.1139/cjp-2013-0457 ◽

2014 ◽

Vol 92 (9) ◽

pp. 1033-1042 ◽

Cited By ~ 4

Author(s):

S. Gupta ◽

R. Kumar ◽

R.P. Malik

Keyword(s):

Gauge Theory ◽

Brst Symmetry ◽

Point Of View ◽

Abelian Gauge ◽

Gauge Invariant ◽

Abelian Gauge Theory ◽

Gauge Transformations ◽

Yang Mills ◽

Symmetry Transformations ◽

Augmented Superfield Formalism

In the available literature, only the Becchi–Rouet–Stora–Tyutin (BRST) symmetries are known for the Jackiw–Pi model of the three (2 + 1)-dimensional (3D) massive non-Abelian gauge theory. We derive the off-shell nilpotent [Formula: see text] and absolutely anticommuting (sbsab + sabsb = 0) (anti-)BRST transformations s(a)b corresponding to the usual Yang–Mills gauge transformations of this model by exploiting the “augmented” superfield formalism where the horizontality condition and gauge invariant restrictions blend together in a meaningful manner. There is a non-Yang–Mills (NYM) symmetry in this theory, too. However, we do not touch the NYM symmetry in our present endeavor. This superfield formalism leads to the derivation of an (anti-)BRST invariant Curci–Ferrari restriction, which plays a key role in the proof of absolute anticommutativity of s(a)b. The derivation of the proper anti-BRST symmetry transformations is important from the point of view of geometrical objects called gerbes. A novel feature of our present investigation is the derivation of the (anti-)BRST transformations for the auxiliary field ρ from our superfield formalism, which is neither generated by the (anti-)BRST charges nor obtained from the requirements of nilpotency and (or) absolute anticommutativity of the (anti-)BRST symmetries for our present 3D non-Abelian 1-form gauge theory.

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