scholarly journals Generalized nonlinear sigma model approach to alternating spin chains and ladders

2000 ◽  
Vol 14 (1) ◽  
pp. 47-52 ◽  
Author(s):  
M. Bocquet ◽  
Th. Jolicoeur
Keyword(s):  
Sigma Model ◽  
Spin Chains ◽  
Nonlinear Sigma Model ◽  
Model Approach

RENORMALIZATION GROUP FLOW AND OPEN STRING DYNAMICS

1988 ◽  
Vol 03 (18) ◽  
pp. 1797-1805 ◽  
Author(s):  
NAOHITO NAKAZAWA ◽  
KENJI SAKAI ◽  
JIRO SODA
Keyword(s):  
Renormalization Group ◽  
Sigma Model ◽  
Open String ◽  
Tree Level ◽  
Nonlinear Sigma Model ◽  
Renormalization Group Flow ◽  
Point Solution ◽  
Β Function ◽  
Group Flow ◽  
Model Approach

The renormalization group flow in the nonlinear sigma model approach is explicitly solved to the fourth order in the case of an open string propagating in the tachyon background. Using a regularization different from the original one used by Klebanov and Susskind (K-S), we show that its fixed point solution produces the tree-level 5-point tachyon amplitude. Furthermore we prove K-S’s conjecture, i.e., the equivalence between the vanishing β-function defined by our regularization and the equation of motion arising from the effective action, up to all orders.

scholarly journals HADRONIC STRING, CONFORMAL INVARIANCE AND CHIRAL SYMMETRY

2003 ◽  
Vol 18 (14) ◽  
pp. 2501-2539 ◽  
Author(s):  
J. ALFARO ◽  
L. BALART ◽  
A. A. ANDRIANOV ◽  
D. ESPRIU
Keyword(s):  
String Theory ◽  
Sigma Model ◽  
Conformal Anomaly ◽  
Nonlinear Sigma Model ◽  
Leading Order ◽  
Qcd Vacuum ◽  
Fundamental String ◽  
Supersymmetric Version ◽  
Long Time ◽  
Model Approach

While it is clear that in some kinematic regime QCD can be described by an effective (as opposed to fundamental) string theory, it is not at all clear how this string theory should be. The "natural" candidate, the bosonic string, leads to amplitudes with the usual problems related to the existence of the tachyon, the absence of the adequate Adler zero, and massless vector particles, not to mention the conformal anomaly. The supersymmetric version does not really solve most of these problems. For a long time it has been believed that the solution of at least some of these difficulties is associated to a proper identification of the vacuum, but this program has remained elusive. We show in this work how the first three problems can be avoided, by using a sigma model approach where excitations above the correct (chirally noninvariant) QCD vacuum are identified. At the leading order in a derivative expansion we recover the nonlinear sigma model of pion interactions. At the next-to-leading order the O(p4) Lagrangian of Gasser and Leutwyler is obtained, with values for the coefficients that match the observed values. We also discuss some issues related to the conformal anomaly.

scholarly journals NONLINEAR SIGMA MODEL APPROACH FOR PHASE DISORDER TRANSITIONS IN CHIRAL GROSS–NEVEU, NAMBU–JONA-LASINIO MODELS AND STRONG-COUPLING SUPERCONDUCTORS

2001 ◽  
Vol 16 (07) ◽  
pp. 1175-1197 ◽  
Author(s):  
EGOR BABAEV
Keyword(s):  
Phase Transition ◽  
Strong Coupling ◽  
Sigma Model ◽  
High Energy ◽  
Bcs Theory ◽  
Nonlinear Sigma Model ◽  
Chiral Phase ◽  
Chiral Phase Transition ◽  
Pseudogap Phase ◽  
Model Approach

We briefly review the nonlinear sigma model approach for the subject of increasing interest: "two-step" phase transitions in the Gross–Neveu and the modified Nambu–Jona-Lasinio models at low N and condensation from pseudogap phase in strong-coupling superconductors. Recent success in describing of "Bose-type" superconductors that possess two characteristic temperatures and a pseudogap above Tc is the development approximately comparable with the BCS theory. One can expect that it should have influence on high-energy physics, similar to impact of the BCS theory on this subject. Although first generalizations of this concept to particle physics were made recently, these results were not systematized. In this review we summarize this development and discuss similarities and differences of the appearance of the pseudogap phase in superconductors and the Gross–Neveu and Nambu–Jona-Lasinio-like models. We discuss its possible relevance for chiral phase transition in QCD and color superconductors. This paper is organized in three parts. In the first part, we briefly review the separation of temperatures of pair formation and pair condensation in strong-coupling and low carrier density superconductors (i.e. the formation of the pseudogap phase). The second part is a review of nonlinear sigma model approach to an analogous phenomenon in the chiral Gross–Neveu model at small N. In the third part we discuss the modified Nambu–Jona-Lasinio model where the chiral phase transition is accompanied by a formation of a phase analogous to the pseudogap phase.

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.

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