A CONDENSED MATTER ANALOG OF QCD WITH QUARKS

1994 ◽  
Vol 08 (04) ◽  
pp. 417-428
Author(s):  
R. SHANKAR
Keyword(s):  
Relativistic Theory ◽  
Sigma Model ◽  
Condensed Matter ◽  
Quantum Spin ◽  
Spin Chains ◽  
Nonlinear Sigma Model ◽  
Dirac Fermions ◽  
Quantum Spin Chains ◽  
Yang Mills ◽  
Gauge Interaction

It is well known that the d = 1 + 1 nonlinear sigma model is a remarkable analog of pure Yang-Mills theory in d = 3 + 1 and that the former in turn arises in the study of Quantum Spin Chains. It is shown that, upon doping with holes, the chain is described by a fully relativistic theory of Dirac fermions coupled to the sigma model by a gauge interaction. The theory is seen to mimic QCD with quarks in many remarkable ways.

scholarly journals q-DEFORMATIONS OF QUANTUM SPIN CHAINS WITH EXACT VALENCE-BOND GROUND STATES

1994 ◽  
Vol 08 (25n26) ◽  
pp. 3645-3654 ◽  
Author(s):  
M.T. BATCHELOR ◽  
C.M. YUNG
Keyword(s):  
Condensed Matter ◽  
Valence Bond ◽  
Ground States ◽  
Quantum Spin ◽  
Total Spin ◽  
Spin Chains ◽  
The Other ◽  
Condensed Matter Physics ◽  
Spin States ◽  
Quantum Spin Chains

Quantum spin chains with exact valence-bond ground states are of great interest in condensed-matter physics. A class of such models was proposed by Affleck et al., each of which is su(2)-invariant and constructed as a sum of projectors onto definite total spin states at neighboring sites. We propose to use the machinery of the q-deformation of su(2) to obtain generalisations of such models, and work out explicitly the two simplest examples. In one case we recover the known anisotropic spin-1 VBS model while in the other we obtain a new anisotropic generalisation of the spin-½ Majumdar-Ghosh model.

scholarly journals ASPECTS OF INTEGRABILITY IN $\mathcal{N} = 4$ SYM

2007 ◽  
Vol 22 (34) ◽  
pp. 2549-2563 ◽  
Author(s):  
ABHISHEK AGARWAL
Keyword(s):  
Gauge Theory ◽  
Integrable Systems ◽  
Closed String ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Four Dimensions ◽  
Yang Mills ◽  
Open Strings

Various recently developed connections between supersymmetric Yang–Mills theories in four dimensions and two-dimensional integrable systems serve as crucial ingredients in improving our understanding of the AdS/CFT correspondence. In this review, we highlight some connections between superconformal four-dimensional Yang–Mills theory and various integrable systems. In particular, we focus on the role of Yangian symmetries in studying the gauge theory dual of closed string excitations. We also briefly review how the gauge theory connects to Calogero models and open quantum spin chains through the study of the gauge theory duals of D3 branes and open strings ending on them. This invited review is based on a seminar given at the Institute of Advanced Study, Princeton.

Solvable nineteen-vertex models and quantum spin chains of spin one

1994 ◽  
Vol 4 (8) ◽  
pp. 1151-1159 ◽  
Author(s):  
Makoto Idzumi ◽  
Tetsuji Tokihiro ◽  
Masao Arai
Keyword(s):  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Vertex Models

scholarly journals Massive gravity from double copy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Arshia Momeni ◽  
Justinas Rumbutis ◽  
Andrew J. Tolley
Keyword(s):  
Sigma Model ◽  
Massive Gravity ◽  
Effective Field ◽  
Effective Theory ◽  
Nonlinear Sigma Model ◽  
Limit Theory ◽  
Four Dimensions ◽  
Yang Mills ◽  
Massive Spin ◽  
Double Copy

Abstract We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions are consistent with a Λ3 = (m2MPl)1/3 cutoff. We construct explicitly the Λ3 decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard Λ3 massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory. This demonstrates that the decoupling limit and double copy procedures do not commute and we clarify why this is the case in terms of the scaling of their kinematic factors.

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