Non‐Abelian solitons in two‐dimensional lattice field theories

1993 ◽  
Vol 34 (12) ◽  
pp. 5560-5588
Author(s):  
V. F. Müller
Keyword(s):  
Field Theories ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Lattice Field

scholarly journals ON TWO-DIMENSIONAL QUASITOPOLOGICAL FIELD THEORIES

2009 ◽  
Vol 24 (32) ◽  
pp. 6105-6121 ◽  
Author(s):  
P. TEOTONIO-SOBRINHO ◽  
C. MOLINA ◽  
N. YOKOMIZO
Keyword(s):  
Hopf Algebras ◽  
Gauge Theories ◽  
Local Symmetry ◽  
Two Dimensions ◽  
Field Theories ◽  
Partition Functions ◽  
Wilson Loops ◽  
Two Dimensional ◽  
Lattice Field ◽  
Expected Values

We study a class of lattice field theories in two dimensions that includes gauge theories. We show that in these theories it is possible to implement a broader notion of local symmetry, based on semisimple Hopf algebras. A character expansion is developed for the quasitopological field theories, and partition functions are calculated with this tool. Expected values of generalized Wilson loops are defined and studied with the character expansion.

scholarly journals QUASITOPOLOGICAL FIELD THEORIES IN TWO DIMENSIONS AS SOLUBLE MODELS

1998 ◽  
Vol 13 (21) ◽  
pp. 3667-3689 ◽  
Author(s):  
BRUNO G. CARNEIRO DA CUNHA ◽  
PAULO TEOTONIO-SOBRINHO
Keyword(s):  
Orientable Surface ◽  
Two Dimensions ◽  
Field Theories ◽  
Partition Functions ◽  
Two Dimensional ◽  
Yang Mills ◽  
Lattice Field ◽  
Topological Field ◽  
Universality Classes ◽  
Area Limit

We study a class of lattice field theories in two dimensions that includes Yang–Mills and generalized Yang–Mills theories as particular examples. Given a two-dimensional orientable surface of genus g, the partition function Z is defined for a triangulation consisting of n triangles of size ∊. The reason these models are called quasitopological is that Z depends on g, n and ∊ but not on the details of the triangulation. They are also soluble in the sense that the computation of their partition functions for a two-dimensional lattice can be reduced to a soluble one-dimensional problem. We show that the continuum limit is well defined if the model approaches a topological field theory in the zero area limit, i.e. ∊→0 with finite n. We also show that the universality classes of such quasitopological lattice field theories can be easily classified.

scholarly journals BMS field theories and Weyl anomaly

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Arjun Bagchi ◽  
Sudipta Dutta ◽  
Kedar S. Kolekar ◽  
Punit Sharma
Keyword(s):  
Three Dimensions ◽  
Field Theories ◽  
Partition Functions ◽  
Two Dimensional ◽  
Speed Of Light ◽  
Asymptotically Flat ◽  
Weyl Invariance ◽  
Flat Spacetimes ◽  
Liouville Action ◽  
Null Surfaces

Abstract Two dimensional field theories with Bondi-Metzner-Sachs symmetry have been proposed as duals to asymptotically flat spacetimes in three dimensions. These field theories are naturally defined on null surfaces and hence are conformal cousins of Carrollian theories, where the speed of light goes to zero. In this paper, we initiate an investigation of anomalies in these field theories. Specifically, we focus on the BMS equivalent of Weyl invariance and its breakdown in these field theories and derive an expression for Weyl anomaly. Considering the transformation of partition functions under this symmetry, we derive a Carrollian Liouville action different from ones obtained in the literature earlier.

scholarly journals Defects and perturbation

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Enrico M. Brehm
Keyword(s):  
Entanglement Entropy ◽  
Topological Defects ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field

Abstract We investigate perturbatively tractable deformations of topological defects in two-dimensional conformal field theories. We perturbatively compute the change in the g-factor, the reflectivity, and the entanglement entropy of the conformal defect at the end of these short RG flows. We also give instances of such flows in the diagonal Virasoro and Super-Virasoro Minimal Models.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

Overrelaxation algorithms for lattice field theories

1988 ◽  
Vol 37 (2) ◽  
pp. 458-471 ◽  
Author(s):  
Stephen L. Adler
Keyword(s):  
Field Theories ◽  
Lattice Field
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