scholarly journals On a gauge-invariant deformation of a classical gauge-invariant theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
I. L. Buchbinder ◽  
P. M. Lavrov
Keyword(s):  
Field Theory ◽  
General Solution ◽  
Generating Functions ◽  
Classical Action ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Higher Spin ◽  
Non Local ◽  
Deformation Procedure ◽  
General Gauge

Abstract We consider a general gauge theory with independent generators and study the problem of gauge-invariant deformation of initial gauge-invariant classical action. The problem is formulated in terms of BV-formalism and is reduced to describing the general solution to the classical master equation. We show that such general solution is determined by two arbitrary generating functions of the initial fields. As a result, we construct in explicit form the deformed action and the deformed gauge generators in terms of above functions. We argue that the deformed theory must in general be non-local. The developed deformation procedure is applied to Abelian vector field theory and we show that it allows to derive non-Abelain Yang-Mills theory. This procedure is also applied to free massless integer higher spin field theory and leads to local cubic interaction vertex for such fields.

scholarly journals Diluted mass gap in strongly coupled non-local Yang-Mills

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Marco Frasca ◽  
Anish Ghoshal
Keyword(s):  
Field Theory ◽  
Particle Physics ◽  
Mass Scale ◽  
Local Theory ◽  
Quantum Field ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Mass Gap ◽  
Non Local ◽  
Non Locality

Abstract We investigate the non-perturbative regimes in the class of non-Abelian theories that have been proposed as an ultraviolet completion of 4-D Quantum Field Theory (QFT) generalizing the kinetic energy operators to an infinite series of higher-order derivatives inspired by string field theory. We prove that, at the non-perturbative level, the physical spectrum of the theory is actually corrected by the “infinite number of derivatives” present in the action. We derive a set of Dyson-Schwinger equations in differential form, for correlation functions till two-points, the solution for which are known in the local theory. We obtain that just like in the local theory, the non-local counterpart displays a mass gap, depending also on the mass scale of non-locality, and show that it is damped in the deep UV asymptotically. We point out some possible implications of our result in particle physics and cosmology and discuss aspects of non-local QCD-like scenarios.

scholarly journals Type II superstring field theory with cyclic $L_\infty$ structure

2020 ◽  
Vol 2020 (3) ◽  
Author(s):  
H Kunimoto ◽  
T Sugimoto
Keyword(s):  
Field Theory ◽  
Hilbert Space ◽  
String Field Theory ◽  
Symplectic Form ◽  
Closed String ◽  
Type Ii ◽  
Gauge Invariant ◽  
Non Local ◽  
String Amplitudes ◽  
Algebraic Formulation

Abstract We construct a complete type II superstring field theory that includes all the NS–NS, R–NS, NS–R, and R–R sectors. As in the open and heterotic superstring cases, the R–NS, NS–R, and R–R string fields are constrained by using the picture-changing operators. In particular, we use a non-local inverse picture-changing operator for the constraint on the R–R string field, which seems to be inevitable due to the compatibility of the extra constraint with the closed string constraints. The natural symplectic form in the restricted Hilbert space gives a non-local kinetic action for the R–R sector, but it correctly provides the propagator expected from the first-quantized formulation. Extending the prescription previously obtained for the heterotic string field theory, we give a construction of general type II superstring products, which realizes a cyclic $L_\infty$ structure, and thus provides a gauge-invariant action based on the homotopy algebraic formulation. Three typical four-string amplitudes derived from the constructed string field theory are demonstrated to agree with those in the first-quantized formulation. We also give the half-Wess–Zumino–Witten action defined in the medium Hilbert space whose left-moving sector is still restricted to the small Hilbert space.

scholarly journals Gauge invariant perturbation theory via homotopy transfer

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Christoph Chiaffrino ◽  
Olaf Hohm ◽  
Allison F. Pinto
Keyword(s):  
Perturbation Theory ◽  
Lie Algebras ◽  
Closed String ◽  
Cosmological Perturbation ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Cosmological Perturbation Theory ◽  
Invariant Perturbation Theory ◽  
General Gauge ◽  
Algorithmic Procedure

Abstract We show that the perturbative expansion of general gauge theories can be expressed in terms of gauge invariant variables to all orders in perturbations. In this we generalize techniques developed in gauge invariant cosmological perturbation theory, using Bardeen variables, by interpreting the passing over to gauge invariant fields as a homotopy transfer of the strongly homotopy Lie algebras encoding the gauge theory. This is illustrated for Yang-Mills theory, gravity on flat and cosmological backgrounds and for the massless sector of closed string theory. The perturbation lemma yields an algorithmic procedure to determine the higher corrections of the gauge invariant variables and the action in terms of these.

scholarly journals n-Point Functions of 2d Yang–Mills Theories on Riemann Surfaces

1997 ◽  
Vol 12 (11) ◽  
pp. 1959-1965 ◽  
Author(s):  
M. Alimohammadi ◽  
M. Khorrami
Keyword(s):  
Field Theory ◽  
Riemann Surfaces ◽  
Integral Method ◽  
Free Field ◽  
Green Functions ◽  
Two Dimensional ◽  
Gauge Invariant ◽  
Gauge Groups ◽  
Yang Mills ◽  
Path Integral Method

Using the simple path integral method we calculate the n-point functions of field strength of Yang–Mills theories on arbitrary two-dimensional Riemann surfaces. In U(1) case we show that the correlators consist of two parts, a free and an x-independent part. In the case of non-Abelian semisimple compact gauge groups we find the nongauge-invariant correlators in Schwinger–Fock gauge and show that it is also divided to a free and an almost x-independent part. We also find the gauge-invariant Green functions and show that they correspond to a free field theory.

scholarly journals Higher spin glueballs from functional methods

2021 ◽  
Vol 81 (12) ◽  
Author(s):  
Markus Q. Huber ◽  
Christian S. Fischer ◽  
Hèlios Sanchis-Alepuz
Keyword(s):  
Excited States ◽  
Positive Charge ◽  
Quantitative Agreement ◽  
Gauge Invariant ◽  
Good Quantitative Agreement ◽  
Yang Mills ◽  
Functional Methods ◽  
Higher Spin ◽  
Charge Parity ◽  
Glueball Spectrum

AbstractWe calculate the glueball spectrum for spin up to $$J=$$ J = 4 and positive charge parity in pure Yang–Mills theory. We construct the full bases for $$J=$$ J = 0, 1, 2, 3, 4 and discuss the relation to gauge invariant operators. Using a fully self-contained truncation of Dyson–Schwinger equations as input, we obtain ground states and first and second excited states from extrapolations of the eigenvalue curves. Where available, we find good quantitative agreement with lattice results

NEW METHODS IN QUANTUM NON-LOCAL FIELD THEORY

1992 ◽  
Vol 07 (21) ◽  
pp. 1895-1904 ◽  
Author(s):  
N.J. CORNISH
Keyword(s):  
Field Theory ◽  
Local Field ◽  
Underlying Structure ◽  
Yang Mills ◽  
Local Gauge ◽  
Functional Methods ◽  
Local Field Theory ◽  
Local Gauge Symmetry ◽  
Non Local ◽  
Insight Into

Functional methods are developed which serve to simplify greatly the calculations in quantum non-local field theory (QNFT). The techniques also serve to give an insight into the underlying structure of QNFT. We show that a transformation can be defined which relates the QNFT Lagrangian to its local antecedent. We prove that the non-local extension of the local gauge symmetry can be obtained by applying this transformation to the local gauge transformation. The utility of this method is demonstrated by an explicit application to both scalar electrodynamics and Yang-Mills field theory.

scholarly journals A master exceptional field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Sigma Model ◽  
Linear Equations ◽  
Field Theories ◽  
Gauge Invariant ◽  
Non Linear ◽  
Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

scholarly journals Perturbative linearization of super-Yang-Mills theories in general gauges

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Hannes Malcha ◽  
Hermann Nicolai
Keyword(s):  
Large Class ◽  
Fourth Order ◽  
Landau Gauge ◽  
Third Order ◽  
Yang Mills ◽  
Free Theory ◽  
Non Linear ◽  
Functional Measure ◽  
Non Local ◽  
Jacobi Determinant

Abstract Supersymmetric Yang-Mills theories can be characterized by a non-local and non-linear transformation of the bosonic fields (Nicolai map) mapping the interacting functional measure to that of a free theory, such that the Jacobi determinant of the transformation equals the product of the fermionic determinants obtained by integrating out the gauginos and ghosts at least on the gauge hypersurface. While this transformation has been known so far only for the Landau gauge and to third order in the Yang-Mills coupling, we here extend the construction to a large class of (possibly non-linear and non-local) gauges, and exhibit the conditions for all statements to remain valid off the gauge hypersurface. Finally, we present explicit results to second order in the axial gauge and to fourth order in the Landau gauge.

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