scholarly journals GAUGE FIELD THEORY ON THE Eq(2)-COVARIANT PLANE

2004 ◽  
Vol 19 (20) ◽  
pp. 3349-3375 ◽  
Author(s):  
FRANK MEYER ◽  
HAROLD STEINACKER
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Differential Calculus ◽  
Euclidean Plane ◽  
Star Product ◽  
Gauge Field Theory ◽  
Two Dimensional ◽  
Suitable Measure ◽  
Natural Way ◽  
Invariant Integration

Gauge theory on the q-deformed two-dimensional Euclidean plane [Formula: see text] is studied using two different approaches. We first formulate the theory using the natural algebraic structures on [Formula: see text], such as a covariant differential calculus, a frame of one-forms and invariant integration. We then consider a suitable star product, and introduce a natural way to implement the Seiberg–Witten map. In both approaches, gauge invariance requires a suitable "measure" in the action, breaking the Eq(2)-invariance. Some possibilities to avoid this conclusion using additional terms in the action are proposed.

scholarly journals Cutoff AdS3 versus $$ T\overline{T} $$ CFT2 in the large central charge sector: correlators of energy-momentum tensor

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yi Li ◽  
Yang Zhou
Keyword(s):  
Field Theory ◽  
Euclidean Plane ◽  
Energy Momentum Tensor ◽  
Central Charge ◽  
Momentum Tensor ◽  
Two Dimensional ◽  
Conformal Field ◽  
Operator Identity ◽  
Pure Gravity ◽  
Charge Sector

Abstract In this article we probe the proposed holographic duality between $$ T\overline{T} $$ T T ¯ deformed two dimensional conformal field theory and the gravity theory of AdS3 with a Dirichlet cutoff by computing correlators of energy-momentum tensor. We focus on the large central charge sector of the $$ T\overline{T} $$ T T ¯ CFT in a Euclidean plane and a sphere, and compute the correlators of energy-momentum tensor using an operator identity promoted from the classical trace relation. The result agrees with a computation of classical pure gravity in Euclidean AdS3 with the corresponding cutoff surface, given a holographic dictionary which identifies gravity parameters with $$ T\overline{T} $$ T T ¯ CFT parameters.

scholarly journals ONE-ELECTRON SPECTRAL WEIGHT OF DOPED MOTT INSULATORS IN GAUGE FIELD THEORY APPROACH

1996 ◽  
Vol 10 (27) ◽  
pp. 3727-3736
Author(s):  
H.C. LEE
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Spectral Weight ◽  
Low Energy ◽  
Vertex Correction ◽  
Gauge Field Theory ◽  
Mott Insulators ◽  
Theory Approach ◽  
Two Dimensional ◽  
Second Order Perturbation Theory

The electron spectral weight of doped Mott insulators based on the two-dimensional slave boson gauge field theory is studied. The vertex correction with static gauge field is calculated in the second order perturbation theory. The vertex correction is found to be singular at low energy and requires non-perturbative treatments.

scholarly journals ON BORWEIN’S CONJECTURES FOR PLANAR UNIFORM RANDOM WALKS

2019 ◽  
Vol 107 (3) ◽  
pp. 392-411 ◽  
Author(s):  
YAJUN ZHOU
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Random Walks ◽  
Euclidean Plane ◽  
Feynman Diagrams ◽  
Quantum Field ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Uniformly Convergent

Let $p_{n}(x)=\int _{0}^{\infty }J_{0}(xt)[J_{0}(t)]^{n}xt\,dt$ be Kluyver’s probability density for $n$-step uniform random walks in the Euclidean plane. Through connection to a similar problem in two-dimensional quantum field theory, we evaluate the third-order derivative $p_{5}^{\prime \prime \prime }(0^{+})$ in closed form, thereby giving a new proof for a conjecture of J. M. Borwein. By further analogies to Feynman diagrams in quantum field theory, we demonstrate that $p_{n}(x),0\leq x\leq 1$ admits a uniformly convergent Maclaurin expansion for all odd integers $n\geq 5$, thus settling another conjecture of Borwein.

scholarly journals Effective Abelian-Higgs Theory from SU(2) gauge field theory

2005 ◽  
Vol 20 (15) ◽  
pp. 3481-3487 ◽  
Author(s):  
VLADIMIR DZHUNUSHALIEV ◽  
DOUGLAS SINGLETON ◽  
DANNY DHOKARH
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Scalar Field ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Mass Term ◽  
Gauge Field Theory ◽  
Ginzburg Landau ◽  
Flux Tubes ◽  
Color Confinement

In the present work we show that it is possible to arrive at a Ginzburg-Landau (GL) like equation from pure SU (2) gauge theory. This has a connection to the dual superconducting model for color confinement where color flux tubes permanently bind quarks into color neutral states. The GL Lagrangian with a spontaneous symmetry breaking potential, has such (Nielsen-Olesen) flux tube solutions. The spontaneous symmetry breaking requires a tachyonic mass for the effective scalar field. Such a tachyonic mass term is obtained from the condensation of ghost fields.

THE FLAT OSp(1,2/2) SUPERCONNECTION CONDITION: 2−d SUPERGRAVITY AND TOPOLOGICAL 2−d GRAVITY

1994 ◽  
Vol 09 (26) ◽  
pp. 2399-2410
Author(s):  
M. LAGRAA
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Gauge Field ◽  
Gauge Field Theory ◽  
Quantum Action

We consider pure 2−d supergravity as a flat OSp (1,2/2) superconnection of a super-gauge field theory on a (2, 2)−d supermanifold. From an appropriate Wigner-Inonu contraction of the OSp (1,2/2) algebra, we show that the superzweibein [Formula: see text] and the U(1) superconnection ΩM of 2−d supergravity transmute into BRST multiplets composed of the fields, their ghosts and the auxiliary fields of gauge theory of topological 2−d gravity. These fields and their topological BRST transformations can be recast in this geometric formalism where the “gravitino” now plays the role of ghost related to the zweibein shift of topological 2−d gravity. We close this paper by constructing a gauge fixed term of the quantum action in terms of superfield.

scholarly journals Chern-Simons gauge field theory of two-dimensional ferromagnets

1993 ◽  
Vol 48 (21) ◽  
pp. 15787-15791 ◽  
Author(s):  
L. Martina ◽  
O. K. Pashaev ◽  
G. Soliani
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Gauge Field Theory ◽  
Two Dimensional ◽  
Chern Simons

scholarly journals Lattice gauge field theory and prismatic sets

2011 ◽  
Vol 108 (1) ◽  
pp. 26 ◽  
Author(s):  
B. Akyar ◽  
J. L. Dupont
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Lie Group ◽  
Lattice Gauge Theory ◽  
Parallel Transport ◽  
Gauge Field Theory ◽  
Classifying Space ◽  
Simplicial Sets ◽  
Lattice Gauge ◽  
Simplicial Set

We study prismatic sets analogously to simplicial sets except that realization involves prisms, i.e., products of simplices rather than just simplices. Particular examples are the prismatic subdivision of a simplicial set $S$ and the prismatic star of $S$. Both have the same homotopy type as $S$ and in particular the latter we use to study lattice gauge theory in the sense of Phillips and Stone. Thus for a Lie group $G$ and a set of parallel transport functions defining the transition over faces of the simplices, we define a classifying map from the prismatic star to a prismatic version of the classifying space of $G$. In turn this defines a $G$-bundle over the prismatic star.

scholarly journals Spacetime duality and two-dimensional gauge field theory

1999 ◽  
Vol 465 (1-4) ◽  
pp. 163-168
Author(s):  
A. Smailagic ◽  
Euro Spallucci
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Gauge Field Theory ◽  
Two Dimensional

O(2) CHERN–SIMONS GAUGE THEORY AND Z2 ORBIFOLDS

1992 ◽  
Vol 07 (05) ◽  
pp. 1007-1023 ◽  
Author(s):  
KAORU AMANO ◽  
HIROSHI SHIROKURA
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Coherent State ◽  
Gauge Field ◽  
Three Dimensional ◽  
The State ◽  
Explicit Calculation ◽  
Gauge Field Theory ◽  
State Representation ◽  
Chern Simons

We quantize the three-dimensional O(2) pure Chern–Simons gauge field theory in a functional coherent-state representation. Both trivial and nontrivial flat O(2) bundles admit physical states. An explicit calculation relates the state functionals to the rational Z2-orbifold models.

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