scholarly journals Construction of supercharges for the one-dimensional supersymmetric nonlinear sigma model

1999 ◽  
Vol 1999 (06) ◽  
pp. 005-005
Author(s):  
Alan J Macfarlane ◽  
Arthur J Mountain
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
One Dimensional ◽  
The One ◽  
Supersymmetric Nonlinear Sigma Model

scholarly journals ON THE QUANTIZATION OF THE N = 2 SUPERSYMMETRIC NONLINEAR SIGMA MODEL

1993 ◽  
Vol 08 (19) ◽  
pp. 3359-3369 ◽  
Author(s):  
G. ALDAZABAL ◽  
J. M. MALDACENA
Keyword(s):  
Operator Product Expansion ◽  
Sigma Model ◽  
Superconformal Algebra ◽  
Operator Product ◽  
Nonlinear Sigma Model ◽  
Coordinate Transformations ◽  
Supersymmetric Nonlinear Sigma Model

A method for quantizing the bidimensional N = 2 supersymmetric nonlinear sigma model is developed. This method is both covariant under coordinate transformations (concerning the order relevant for calculation) and explicitly N = 2 supersymmetric. The operator product expansion of the supercurrent is computed accordingly, including also the dilaton. By imposing the N = 2 superconformal algebra the equations for the metric and the dilaton are obtained. In particular, they imply that the dilaton is a constant.

scholarly journals METAPLECTIC SPINOR FIELDS AND GLOBAL ANOMALIES

1995 ◽  
Vol 10 (01) ◽  
pp. 65-88 ◽  
Author(s):  
M. REUTER
Keyword(s):  
Phase Space ◽  
Sigma Model ◽  
Target Space ◽  
Spin Manifold ◽  
Nonlinear Sigma Model ◽  
Metaplectic Representation ◽  
One Dimensional ◽  
Path Integral Representation ◽  
Infinite Dimensional ◽  
Spinor Fields

We investigate spinor fields on phase spaces. Under local frame rotations they transform according to the (infinite-dimensional, unitary) metaplectic representation of Sp(2N), which plays a role analogous to the Lorentz group. We introduce a one-dimensional nonlinear sigma model whose target space is the phase space under consideration. The global anomalies of this model are analyzed, and it is shown that its fermionic partition function is anomalous exactly if the underlying phase space is not a spin manifold, i.e. if metaplectic spinor fields cannot be introduced consistently. The sigma model is constructed by giving a path integral representation to the Lie transport of spinors along the Hamiltonian flow.

HUBBARD CHAIN EXTENDED TO INCORPORATE THE PEIERLS INSTABILITY

1992 ◽  
Vol 06 (11) ◽  
pp. 637-647
Author(s):  
ADRIAAN M. J. SCHAKEL
Keyword(s):  
Sigma Model ◽  
Qualitative Difference ◽  
Fundamental Property ◽  
Nonlinear Sigma Model ◽  
One Dimensional ◽  
Long Wavelength ◽  
Peierls Instability ◽  
Two Phases ◽  
The Continuum ◽  
Topological Term

The Hubbard chain is extended so as to incorporate the Peierls instability which is a fundamental property of one-dimensional metals. The resulting theory is analysed in the continuum. In the limit of low-energy and long-wavelength it is described by the O(3) nonlinear sigma model. It is argued that the theory has two phases. In one phase the excitation spectrum is gapless, while in the other phase it has a gap. This qualitative difference between the two states is shown to arise from the fact that in the massless phase the O(3) model acquires a topological term. Besides changing the spectrum of the theory, this term is shown to also change statistics.

scholarly journals Yang-Baxter and the Boost: splitting the difference

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Marius de Leeuw ◽  
Chiara Paletta ◽  
Anton Pribytok ◽  
Ana L. Retore ◽  
Paul Ryan
Keyword(s):  
Hilbert Space ◽  
Sigma Model ◽  
Spin Chains ◽  
Baxter Equation ◽  
Regular Solutions ◽  
One Dimensional ◽  
Difference Form ◽  
The Difference ◽  
The One

In this paper we continue our classification of regular solutions of the Yang-Baxter equation using the method based on the spin chain boost operator developed in [1]. We provide details on how to find all non-difference form solutions and apply our method to spin chains with local Hilbert space of dimensions two, three and four. We classify all 16\times1616×16 solutions which exhibit \mathfrak{su}(2)\oplus \mathfrak{su}(2)𝔰𝔲(2)⊕𝔰𝔲(2) symmetry, which include the one-dimensional Hubbard model and the SS-matrix of the {AdS}_5 \times {S}^5AdS5×S5 superstring sigma model. In all cases we find interesting novel solutions of the Yang-Baxter equation.

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.

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