scholarly journals EXACT SEIBERG–WITTEN MAP AND INDUCED GRAVITY FROM NONCOMMUTATIVITY

2006 ◽  
Vol 21 (35) ◽  
pp. 2637-2647 ◽  
Author(s):  
HYUN SEOK YANG
Keyword(s):  
Field Theory ◽  
Closed Form ◽  
Gauge Fields ◽  
Induced Gravity ◽  
Spacetime Geometry ◽  
Field Dependent ◽  
Interesting Idea ◽  
Action Coupling

We find a closed form for Seiberg–Witten (SW) map between ordinary and noncommutative (NC) Dirac–Born–Infeld actions. We show that NC Maxwell action after the exact SW map can be regarded as ordinary Maxwell action coupling to a metric deformed by gauge fields. We also show that reversed procedure by inverse SW map lead to a similar interpretation in terms of induced NC geometry. This implies that noncommutativity in field theory can be interpreted as field-dependent fluctuations of spacetime geometry, which genuinely realizes an interesting idea recently observed by Rivelles.

Unification of Gauge Forces and Gravity using Tangled Vortex Knots and Entanglement Dynamics

2020 ◽  
Author(s):  
Mrittunjoy Guha Majumdar
Keyword(s):  
Field Theory ◽  
Short Range ◽  
Gauge Fields ◽  
Entanglement Dynamics ◽  
Unified Field Theory ◽  
Linear Dynamics ◽  
Unified Field ◽  
The Standard Model ◽  
Theory Of Everything ◽  
The Continuum

In this paper, the statistics of excitation-tangles in a postulated background ideal-superfluid field is studied. The structure of the Standard Model is derived in terms of tangle vortex-knots and soliton. Gravity is observed in terms of torsion and curvature in the continuum. In this way, non-linear dynamics and excitations give rise to a unified field theory as well as a Theory of Everything. As a result of this unification, spacetime and matter are shown to be fundamentally equivalent, while gauge fields arise from reorientation and excitations of the the fundamental underlying field. Finally, the equivalence of topological and quantum entanglement is explored to posit a theory of everything in terms of long- and short-range entanglement between fundamental quantum units (bits) of information.

scholarly journals THE UNIVERSAL LINK POLYNOMIAL

1992 ◽  
Vol 07 (05) ◽  
pp. 877-945 ◽  
Author(s):  
E. GUADAGNINI
Keyword(s):  
Field Theory ◽  
Closed Form ◽  
Lie Algebra ◽  
Wilson Line ◽  
Expectation Values ◽  
Simple Lie Algebra ◽  
Chern Simons

The solution of the non-Abelian SU (N) quantum Chern–Simons field theory defined in R3 is presented. It is shown how to compute the expectation values of the Wilson line operators, associated with oriented framed links, in closed form. The main properties of the universal link polynomial, defined by these expectation values, are derived in the case of a generic real simple Lie algebra. The resulting polynomials for some simple examples of links are reported.

Induced Gauge Structure for the Zero Modes of Two-Dimensional Solitons

1997 ◽  
Vol 12 (01) ◽  
pp. 57-64 ◽  
Author(s):  
Yuji Igarashi ◽  
Shinsaku Kitakado ◽  
Hideharu Otsu ◽  
Toshiro Sato
Keyword(s):  
Field Theory ◽  
Gauge Fields ◽  
Two Dimensional ◽  
Zero Modes ◽  
Gauge Structure

The induced gauge structure for the zero modes of two-dimensional solitons is considered bearing in mind the possibility of finding the origin of gauge fields in field theory.

scholarly journals Higher-derivative heterotic Double Field Theory and classical double copy

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Eric Lescano ◽  
Jesús A. Rodríguez
Keyword(s):  
Field Theory ◽  
Exact Solutions ◽  
Maxwell Equations ◽  
Action Principle ◽  
Low Energy ◽  
Gauge Fields ◽  
Metric Tensor ◽  
Higher Derivative ◽  
Double Field Theory ◽  
Double Copy

Abstract The generalized Kerr-Schild ansatz (GKSA) is a powerful tool for constructing exact solutions in Double Field Theory (DFT). In this paper we focus in the heterotic formulation of DFT, considering up to four-derivative terms in the action principle, while the field content is perturbed by the GKSA. We study the inclusion of the generalized version of the Green-Schwarz mechanism to this setup, in order to reproduce the low energy effective heterotic supergravity upon parametrization. This formalism reproduces higher-derivative heterotic background solutions where the metric tensor and Kalb-Ramond field are perturbed by a pair of null vectors. Next we study higher-derivative contributions to the classical double copy structure. After a suitable identification of the null vectors with a pair of U(1) gauge fields, the dynamics is given by a pair of Maxwell equations plus higher derivative corrections in agreement with the KLT relation.

A gauge theory of the Weyl group

1974 ◽  
Vol 340 (1622) ◽  
pp. 249-262 ◽  
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Conservation Laws ◽  
Weyl Group ◽  
Lorentz Group ◽  
Space Time ◽  
Gauge Fields ◽  
Field Equations ◽  
Covariant Derivatives ◽  
The World

The construction of field theory which exhibits invariance under the Weyl group with parameters dependent on space–time is discussed. The method is that used by Utiyama for the Lorentz group and by Kibble for the Poincaré group. The need to construct world-covariant derivatives necessitates the introduction of three sets of gauge fields which provide a local affine connexion and a vierbein system. The geometrical implications are explored; the world geometry has an affine connexion which is not symmetric but is semi-metric. A possible choice of Lagrangian for the gauge fields is presented, and the resulting field equations and conservation laws discussed.

scholarly journals ON THE CORRESPONDENCE BETWEEN NONCOMMUTATIVE FIELD THEORY AND GRAVITY

2007 ◽  
Vol 22 (16) ◽  
pp. 1119-1132 ◽  
Author(s):  
HYUN SEOK YANG
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Gauge Fields ◽  
Noncommutative Field Theory ◽  
Basic Reason ◽  
New Development ◽  
Collective Phenomenon ◽  
Darboux Theorem ◽  
Theory Of Gravity

In this brief review, we summarize the new development on the correspondence between noncommutative (NC) field theory and gravity, shortly referred to as the NCFT/Gravity correspondence. We elucidate why a gauge theory in NC spacetime should be a theory of gravity. A basic reason for the NCFT/Gravity correspondence is that the Λ-symmetry (or B-field transformations) in NC spacetime can be considered as a par with diffeomorphisms, which results from the Darboux theorem. This fact leads to a striking picture about gravity: Gravity can emerge from a gauge theory in NC spacetime. Gravity is then a collective phenomenon emerging from gauge fields living in fuzzy spacetime.

ANYON EQUATION ON A TORUS

1992 ◽  
Vol 07 (23) ◽  
pp. 5797-5831 ◽  
Author(s):  
CHOON-LIN HO ◽  
YUTAKA HOSOTANI
Keyword(s):  
Field Theory ◽  
Wave Function ◽  
Essential Role ◽  
Wilson Line ◽  
Regular Function ◽  
Gauge Fields ◽  
Quantum Field ◽  
Many Body ◽  
Definition Of ◽  
Chern Simons

Starting from the quantum field theory of nonrelativistic matter on a torus interacting with Chern-Simons gauge fields, we derive the Schrödinger equation for an anyon system. The nonintegrable phases of the Wilson line integrals on a torus play an essential role. In addition to generating degenerate vacua, they enter in the definition of a many-body Schrödinger wave function in quantum mechanics, which can be defined as a regular function of the coordinates of anyons. It obeys a non-Abelian representation of the braid group algebra, being related to Einarsson’s wave function by a singular gauge transformation.

scholarly journals Finite field-dependent BRST–anti-BRST transformations: Jacobians and application to the Standard Model

2016 ◽  
Vol 31 (20n21) ◽  
pp. 1650111 ◽  
Author(s):  
Pavel Yu. Moshin ◽  
Alexander A. Reshetnyak
Keyword(s):  
Standard Model ◽  
Gauge Theories ◽  
Landau Gauge ◽  
Gauge Fields ◽  
Nontrivial Solutions ◽  
Abelian Gauge ◽  
The Standard Model ◽  
Field Dependent ◽  
Quantum Action ◽  
General Gauge

We continue our research[Formula: see text] and extend the class of finite BRST–anti-BRST transformations with odd-valued parameters [Formula: see text], [Formula: see text], introduced in these works. In doing so, we evaluate the Jacobians induced by finite BRST–anti-BRST transformations linear in functionally-dependent parameters, as well as those induced by finite BRST–anti-BRST transformations with arbitrary functional parameters. The calculations cover the cases of gauge theories with a closed algebra, dynamical systems with first-class constraints, and general gauge theories. The resulting Jacobians in the case of linearized transformations are different from those in the case of polynomial dependence on the parameters. Finite BRST–anti-BRST transformations with arbitrary parameters induce an extra contribution to the quantum action, which cannot be absorbed into a change of the gauge. These transformations include an extended case of functionally-dependent parameters that implies a modified compensation equation, which admits nontrivial solutions leading to a Jacobian equal to unity. Finite BRST–anti-BRST transformations with functionally-dependent parameters are applied to the Standard Model, and an explicit form of functionally-dependent parameters [Formula: see text] is obtained, providing the equivalence of path integrals in any 3-parameter [Formula: see text]-like gauges. The Gribov–Zwanziger theory is extended to the case of the Standard Model, and a form of the Gribov horizon functional is suggested in the Landau gauge, as well as in [Formula: see text]-like gauges, in a gauge-independent way using field-dependent BRST–anti-BRST transformations, and in [Formula: see text]-like gauges using transverse-like non-Abelian gauge fields.

scholarly journals Linear Yang–Mills Theory as a Homotopy AQFT

2019 ◽  
Vol 378 (1) ◽  
pp. 185-218 ◽  
Author(s):  
Marco Benini ◽  
Simen Bruinsma ◽  
Alexander Schenkel
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Poisson Structure ◽  
Gauge Fields ◽  
Quantum Field ◽  
Lorentzian Manifolds ◽  
Algebraic Quantum Field Theory ◽  
Yang Mills ◽  
Algebraic Quantum ◽  
Klein Gordon

AbstractIt is observed that the shifted Poisson structure (antibracket) on the solution complex of Klein–Gordon and linear Yang–Mills theory on globally hyperbolic Lorentzian manifolds admits retarded/advanced trivializations (analogs of retarded/advanced Green’s operators). Quantization of the associated unshifted Poisson structure determines a unique (up to equivalence) homotopy algebraic quantum field theory (AQFT), i.e. a functor that assigns differential graded $$*$$ ∗ -algebras of observables and fulfills homotopical analogs of the AQFT axioms. For Klein–Gordon theory the construction is equivalent to the standard one, while for linear Yang–Mills it is richer and reproduces the BRST/BV field content (gauge fields, ghosts and antifields).

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