scholarly journals Apparently Noninvariant Terms of U(N) x U(N) Nonlinear Sigma Model in the One-Loop Approximation

2010 ◽  
Vol 123 (3) ◽  
pp. 475-498 ◽  
Author(s):  
K. Harada ◽  
H. Kubo ◽  
Y. Yamamoto
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Loop Approximation ◽  
The One

Non-Abelian BFFT embedding, Schrödinger quantization and the field–antifield anomaly of the O(N) nonlinear sigma model

2016 ◽  
Vol 31 (01) ◽  
pp. 1550225 ◽  
Author(s):  
E. M. C. de Abreu ◽  
J. Ananias Neto ◽  
A. C. R. Mendes ◽  
G. Oliveira-Neto
Keyword(s):  
Excited States ◽  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Quantum Level ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Class System ◽  
Gauge Symmetries ◽  
Nonlocal Field ◽  
The One

We have embedded the [Formula: see text] nonlinear sigma model in a non-Abelian gauge theory. After that as a first class-system, it was quantized using two different approaches: the functional Schrödinger method and the nonlocal field–antifield procedure. First, the quantization was performed with the functional Schrödinger method, for [Formula: see text], obtaining the wave functionals for the ground and excited states. Second, using the well-known BV formalism, we have computed the one-loop anomaly. This result shows that the classical gauge symmetries, which appear due to the conversion via BFFT method, are broken at the quantum level.

THE BOSONIC SIGMA MODEL ON A COMPACT SURFACE

1990 ◽  
Vol 05 (25) ◽  
pp. 2031-2037 ◽  
Author(s):  
M. LEBLANC ◽  
P. MADSEN ◽  
R. B. MANN ◽  
D. G. C. McKEON
Keyword(s):  
Sigma Model ◽  
Stereographic Projection ◽  
Two Dimensions ◽  
Compact Surface ◽  
Three Dimensions ◽  
Dimensional Euclidean Space ◽  
Nonlinear Sigma Model ◽  
Β Function ◽  
The One ◽  
Infrared Divergences

A stereographic projection is used to map the bosonic nonlinear sigma model with torsion from two-dimensional Euclidean space onto a sphere-S2 embedded in three dimensions. The one-loop β-function of the torsionless σ-model is determined using operator regularization to handle ultraviolet divergences. Only by excluding the lowest eigenstate of the rotation operator on the sphere can the usual β-function be recovered; inclusion of this eigenstate leads to severe infrared divergences. Both the ultraviolet and infrared divergences can be regulated by working in n, rather than two, dimensions, in which case the contribution of the lowest mode cancels exactly against the contribution of all other modes, resulting in a vanishing β-function.

Old wine in a new bottle: Technidilaton as the 125 GeV Higgs

2017 ◽  
Vol 32 (36) ◽  
pp. 1747026
Author(s):  
Koichi Yamawaki
Keyword(s):  
Sigma Model ◽  
Local Symmetry ◽  
Effective Theory ◽  
Nonlinear Sigma Model ◽  
Scale Invariant ◽  
Gauge Bosons ◽  
Strongly Coupled ◽  
Technicolor Model ◽  
Vector Bosons ◽  
The One

The first Nagoya SCGT workshop back in 1988 (SCGT 88) was motivated by the walking technicolor and technidilaton. Now at SCGT15 I returned to the “old wine” in “a new bottle”, the recently discovered 125 Higgs boson as the technidilaton. We show that the Standard Model (SM) Higgs Lagrangian is identical to the nonlinear realization of both the scale and chiral symmetries (“scale-invariant nonlinear sigma model”), and is further gauge equivalent to the “scale-invariant Hidden Local Symmetry (HLS) model” having possible new vector bosons as the HLS gauge bosons with scale-invariant mass: SM Higgs is nothing but a (pseudo) dilaton. The effective theory of the walking technicolor has precisely the same type of the scale-invariant nonlinear sigma model, thus further having the scale-invariant HLS gauge bosons (technirho’s, etc.). The technidilaton mass [Formula: see text] comes from the trace anomaly, which yields [Formula: see text] via PCDC, in the underlying walking [Formula: see text] gauge theory with [Formula: see text] massless flavors, where [Formula: see text] is the the decay constant and [Formula: see text]. This implies [Formula: see text] for [Formula: see text] in the one-family walking technicolor model [Formula: see text], in good agreement with the current LHC Higgs data. In the anti-Veneziano limit, [Formula: see text], with [Formula: see text]fixed and [Formula: see text]fixed [Formula: see text], we have a result: [Formula: see text]. Then the technidilaton is a naturally light composite Higgs out of the strongly coupled conformal dynamics, with its couplings even weaker than the SM Higgs. Related holographic and lattice results are also discussed. In particular, such a light flavor-singlet scalar does exists in the lattice simulations in the walking regime.

Spontaneous Compactification Induced by Gravitons and Scalar Field

1997 ◽  
Vol 12 (28) ◽  
pp. 5007-5018
Author(s):  
N. Granda ◽  
E. Loaiza
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Dimensional Sphere ◽  
Minkowski Space Time ◽  
Background Space ◽  
Dimensional Minkowski Space ◽  
The One ◽  
Hilbert Action ◽  
Kaluza Klein ◽  
Made In

We evaluate the one-loop effective potential for the Einstein–Hilbert action coupled to a nonlinear sigma model in a Kaluza–Klein background space M4 × SN (M4 is the four-dimensional Minkowski space–time and SN is the N-dimensional sphere) for odd N. The computation is made in the harmonic and in the light cone gauges. The radius of compactification for some N was found.

BULK SCALAR-FIELD INFLUENCED FRW UNIVERSE MODEL

2012 ◽  
Vol 27 (01) ◽  
pp. 1250003 ◽  
Author(s):  
TAE HOON LEE ◽  
SUNNYEO LEE
Keyword(s):  
Sigma Model ◽  
Scalar Fields ◽  
Einstein Gravity ◽  
Warp Factor ◽  
Nonlinear Sigma Model ◽  
Universe Model ◽  
Frw Universe ◽  
Brane Model ◽  
Bulk Scalar Field ◽  
The One

We consider a nonlinear sigma-model-like theory of bulk scalar fields coupled to the five-dimensional Einstein gravity. In Robertson–Walker spacetimes, we find some power-law cosmological solutions for the scale factor when the expansion rate of an extra dimension is proportional to one of our (3+1)-dimensional universe. Among them, the solution with a decreasing warp factor could be related to the one-brane model of Randall and Sundrum.

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.

scholarly journals An emergent universe supported by a nonlinear sigma model

2009 ◽  
Vol 26 (7) ◽  
pp. 075017 ◽  
Author(s):  
A Beesham ◽  
S V Chervon ◽  
S D Maharaj
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Emergent Universe
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