scholarly journals A Lie algebra for closed strings, spin chains, and gauge theories

1998 ◽  
Vol 39 (10) ◽  
pp. 5199-5230 ◽  
Author(s):  
C.-W. H. Lee ◽  
S. G. Rajeev
Keyword(s):  
Lie Algebra ◽  
Gauge Theories ◽  
Spin Chains

scholarly journals Spectral dualities in XXZ spin chains and five dimensional gauge theories

2013 ◽  
Vol 2013 (12) ◽  
Author(s):  
A. Mironov ◽  
A. Morozov ◽  
B. Runov ◽  
Y. Zenkevich ◽  
A. Zotov
Keyword(s):  
Gauge Theories ◽  
Spin Chains

scholarly journals Lie algebra cohomology and group structure of gauge theories

1996 ◽  
Vol 37 (12) ◽  
pp. 6106-6120 ◽  
Author(s):  
Hyun Seok Yang ◽  
Bum‐Hoon Lee
Keyword(s):  
Lie Algebra ◽  
Gauge Theories ◽  
Group Structure ◽  
Lie Algebra Cohomology

scholarly journals QQ-system and Weyl-type transfer matrices in integrable SO(2r) spin chains

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Gwenäel Ferrando ◽  
Rouven Frassek ◽  
Vladimir Kazakov
Keyword(s):  
Lie Algebra ◽  
Finite Length ◽  
Spin Chains ◽  
Transfer Matrices ◽  
Full System ◽  
Functional Relations ◽  
Integrable Spin ◽  
Integrable Spin Chains

Abstract We propose the full system of Baxter Q-functions (QQ-system) for the integrable spin chains with the symmetry of the Dr Lie algebra. We use this QQ-system to derive new Weyl-type formulas expressing transfer matrices in all symmetric and antisymmetric (fundamental) representations through r + 1 basic Q-functions. Our functional relations are consistent with the Q-operators proposed recently by one of the authors and verified explicitly on the level of operators at small finite length.

scholarly journals GAUGE THEORIES ON OPEN LIE ALGEBRA NONCOMMUTATIVE SPACES

2003 ◽  
Vol 18 (07) ◽  
pp. 491-501
Author(s):  
A. AGARWAL ◽  
L. AKANT
Keyword(s):  
Lie Algebra ◽  
Gauge Theories ◽  
Explicit Construction ◽  
Star Products ◽  
Associative Algebras ◽  
Highly Nonlinear ◽  
Noncommutative Spaces

It is shown that noncommutative spaces, which are quotients of associative algebras by ideals generated by highly nonlinear relations of a particular type, admit extremely simple formulae for deformed or star products. Explicit construction of these star products is carried out. Quantum gauge theories are formulated on these spaces, and the Seiberg–Witten map is worked out in detail.

scholarly journals Bethe/gauge correspondence for SO/Sp gauge theories and open spin chains

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Taro Kimura ◽  
Rui-Dong Zhu
Keyword(s):  
Boundary Conditions ◽  
Gauge Theories ◽  
Spin Chains

Abstract In this article, we extend the work of [1] to a Bethe/Gauge correspondence between 2d (or resp. 3d) SO/Sp gauge theories and open XXX (resp. XXZ) spin chains with diagonal boundary conditions. The case of linear quiver gauge theories is also considered.

scholarly journals THE DILATATION OPERATOR OF $\mathcal{N}=4$ SYM AND CLASSICAL LIMITS OF SPIN CHAINS AND MATRIX MODELS

2004 ◽  
Vol 19 (34) ◽  
pp. 2549-2568 ◽  
Author(s):  
A. AGARWAL ◽  
S. G. RAJEEV
Keyword(s):  
Matrix Models ◽  
Lie Algebra ◽  
Classical Limit ◽  
Quantum Spin ◽  
Spin Chains ◽  
Point Of View ◽  
Hamiltonian Matrix ◽  
Quantum Spin Chains ◽  
Dilatation Operator ◽  
The Matrix

A study of the one-loop dilatation operator in the scalar sector of [Formula: see text] SYM is presented. The dilatation operator is analyzed from the point of view of Hamiltonian matrix models. A Lie algebra underlying operator mixing in the planar large-N limit is presented, and its role in understanding the integrability of the planar dilatation operator is emphasized. A classical limit of the dilatation operator is obtained by considering a contraction of this Lie algebra, leading to a new way of constructing classical limits for quantum spin chains. An infinite tower of local conserved charges is constructed in this classical limit purely within the context of the matrix model. The deformation of these charges and their relation to the charges of the spin chain is also elaborated upon.

scholarly journals GENERALIZED GAUGE THEORIES AND THE WEINBERG–SALAM MODEL WITH DIRAC–KÄHLER FERMIONS

2001 ◽  
Vol 16 (23) ◽  
pp. 3867-3895 ◽  
Author(s):  
NOBORU KAWAMOTO ◽  
HIROSHI UMETSU ◽  
TAKUYA TSUKIOKA
Keyword(s):  
Gauge Theory ◽  
Lie Algebra ◽  
Noncommutative Geometry ◽  
Gauge Theories ◽  
Differential Forms ◽  
Gauge Fields ◽  
Present Formulation ◽  
Yang Mills ◽  
Graded Lie Algebra ◽  
Chern Simons

We extend the previously proposed generalized gauge theory formulation of the Chern–Simons type and topological Yang–Mills type actions into Yang–Mills type actions. We formulate gauge fields and Dirac–Kähler matter fermions by all degrees of differential forms. The simplest version of the model which includes only zero and one-form gauge fields accommodated with the graded Lie algebra of SU (2|1) supergroup leads the Weinberg–Salam model. Thus the Weinberg–Salam model formulated by noncommutative geometry is a particular example of the present formulation.

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