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.

A COMPACT BOSON COUPLED TO TWO-DIMENSIONAL GRAVITY

1991 ◽  
Vol 06 (15) ◽  
pp. 2743-2754 ◽  
Author(s):  
NORISUKE SAKAI ◽  
YOSHIAKI TANII
Keyword(s):  
Field Theory ◽  
Partition Function ◽  
Quantum Gravity ◽  
Matrix Models ◽  
Riemann Surfaces ◽  
Partition Functions ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
The Continuum ◽  
Continuum Field

The radius dependence of partition functions is explicitly evaluated in the continuum field theory of a compactified boson, interacting with two-dimensional quantum gravity (noncritical string) on Riemann surfaces for the first few genera. The partition function for the torus is found to be a sum of terms proportional to R and 1/R. This is in agreement with the result of a discretized version (matrix models), but is quite different from the critical string. The supersymmetric case is also explicitly evaluated.

ON p-ADIC FUNCTIONAL INTEGRALS

1988 ◽  
Vol 03 (06) ◽  
pp. 639-643 ◽  
Author(s):  
GIORGIO PARISI
Keyword(s):  
Field Theory ◽  
Quantum Mechanics ◽  
Free Field ◽  
Two Dimensional ◽  
Functional Integrals

In this letter we present a possible form of quantum mechanics in the case where the dynamical variables (or the time) are p-adic numbers. We also present a possible formulation of two-dimensional free field theory on a two-dimensional p-adic space.

NON-PERTURBAITVE GREEN FUNCTIONS IN QUANTUM GAUGE THEORIES

1991 ◽  
Vol 06 (10) ◽  
pp. 909-921 ◽  
Author(s):  
S.V. SHABANOV
Keyword(s):  
Configuration Space ◽  
Gauge Theories ◽  
Gauge Condition ◽  
Green Functions ◽  
Spatial Infinity ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Global Gauge

Non-perturbative Green functions for gauge invariant variables are considered. The Green functions are found to be modified as compared with the usual ones in a definite gauge because of a physical configuration space (PCS) reduction. In the Yang-Mills theory with fermions, this phenomenon follows from the Singer theorem about the absence of a global gauge condition for the fields tending to zero at spatial infinity.

scholarly journals Exact expressions for n-point maximal U(1)Y-violating integrated correlators in SU(N) $$ \mathcal{N} $$ = 4 SYM

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Daniele Dorigoni ◽  
Michael B. Green ◽  
Congkao Wen
Keyword(s):  
Modular Forms ◽  
Free Field ◽  
Perturbation Expansion ◽  
Flat Space ◽  
Low Energy ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Yang Mills ◽  
Infinite Sums

Abstract The exact expressions for integrated maximal U(1)Y violating (MUV) n-point correlators in SU(N) $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory are determined. The analysis generalises previous results on the integrated correlator of four superconformal primaries and is based on supersymmetric localisation. The integrated correlators are functions of N and τ = θ/(2π) + 4πi/$$ {g}_{YM}^2 $$ g YM 2 , and are expressed as two-dimensional lattice sums that are modular forms with holomorphic and anti-holomorphic weights (w, −w) where w = n − 4. The correlators satisfy Laplace-difference equations that relate the SU(N+1), SU(N) and SU(N−1) expressions and generalise the equations previously found in the w = 0 case. The correlators can be expressed as infinite sums of Eisenstein modular forms of weight (w, −w). For any fixed value of N the perturbation expansion of this correlator is found to start at order ($$ {g}_{YM}^2 $$ g YM 2 N)w. The contributions of Yang-Mills instantons of charge k > 0 are of the form qkf(gYM), where q = e2πiτ and f(gYM) = O($$ {g}_{YM}^{-2w} $$ g YM − 2 w ) when $$ {g}_{YM}^2 $$ g YM 2 ≪ 1. Anti-instanton contributions have charge k < 0 and are of the form $$ {\overline{q}}^{\left|k\right|}\hat{f}\left({g}_{YM}\right) $$ q ¯ k f ̂ g YM , where $$ \hat{f}\left({g}_{YM}\right)=O\left({g}_{YM}^{2w}\right) $$ f ̂ g YM = O g YM 2 w when $$ {g}_{YM}^2 $$ g YM 2 ≪ 1. Properties of the large-N expansion are in agreement with expectations based on the low energy expansion of flat-space type IIB superstring amplitudes. We also comment on the identification of n-point free-field MUV correlators with the integrands of (n − 4)-loop perturbative contributions to the four-point correlator. In particular, we emphasise the important rôle of SL(2, ℤ)-covariance in the construction.

scholarly journals Area-Dependent Quantum Field Theory

2020 ◽  
Author(s):  
Ingo Runkel ◽  
Lóránt Szegedy
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Two Dimensional ◽  
Positive Real ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Frobenius Algebras ◽  
Topological Quantum ◽  
Topological Theories

AbstractArea-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real number—interpreted as area—which behaves additively under glueing. As opposed to topological theories, in area-dependent theories the state spaces can be infinite-dimensional. We introduce the notion of regularised Frobenius algebras in Hilbert spaces and show that area-dependent theories are in one-to-one correspondence to commutative regularised Frobenius algebras. We also provide a state sum construction for area-dependent theories. Our main example is two-dimensional Yang–Mills theory with compact gauge group, which we treat in detail.

scholarly journals Tetrads in SU(3) × SU(2) × U(1) Yang–Mills geometrodynamics

2018 ◽  
Vol 15 (03) ◽  
pp. 1850045 ◽  
Author(s):  
Alcides Garat
Keyword(s):  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Noncompact Group ◽  
Gauge Invariant ◽  
Gauge Groups ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Local Gauge ◽  
Stress Energy ◽  
Local Plane

The relationship between gauge and gravity amounts to understanding the underlying new geometrical local structures. These structures are new tetrads specially devised for Yang–Mills theories, Abelian and non-Abelian in four-dimensional Lorentzian curved spacetimes. In the present paper, a new tetrad is introduced for the Yang–Mills [Formula: see text] formulation. These new tetrads establish a link between local groups of gauge transformations and local groups of spacetime transformations that we previously called LB1 and LB2. New theorems are proved regarding isomorphisms between local internal [Formula: see text] groups and local tensor products of spacetime LB1 and LB2 groups of transformations. These new tetrads define at every point in spacetime two orthogonal planes that we called blades or planes one and two. These are the local planes of covariant diagonalization of the stress–energy tensor. These tetrads are gauge dependent. Tetrad local gauge transformations leave the tetrads inside the local original planes without leaving them. These local tetrad gauge transformations enable the possibility to connect local gauge groups Abelian or non-Abelian with local groups of tetrad transformations. On the local plane one, the Abelian group [Formula: see text] of gauge transformations was already proved to be isomorphic to the tetrad local group of transformations LB1, for example. LB1 is [Formula: see text] plus two different kinds of discrete transformations. On the local orthogonal plane two [Formula: see text] is isomorphic to LB2 which is just [Formula: see text]. That is, we proved that LB1 is isomorphic to [Formula: see text] which is a remarkable result since a noncompact group plus two discrete transformations is isomorphic to a compact group. These new tetrads have displayed manifestly and nontrivially the coupling between Yang–Mills fields and gravity. The new tetrads and the stress–energy tensor allow for the introduction of three new local gauge invariant objects. Using these new gauge invariant objects and in addition a new general local duality transformation, a new algorithm for the gauge invariant diagonalization of the Yang–Mills stress–energy tensor is developed as an application. This is a paper about grand Standard Model gauge theories — General Relativity gravity unification and grand group unification in four-dimensional curved Lorentzian spacetimes.

scholarly journals THE “DUAL” VARIABLES OF YANG-MILLS THEORY AND LOCAL GAUGE-INVARIANT VARIABLES

1996 ◽  
Vol 11 (32) ◽  
pp. 5701-5728 ◽  
Author(s):  
ORI GANOR ◽  
J. SONNENSCHEIN
Keyword(s):  
Degrees Of Freedom ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Six Degrees Of Freedom ◽  
Local Gauge ◽  
Dual Variables ◽  
Topological Part

After adding auxiliary fields and integrating out the original variables, the Yang-Mills action can be expressed in terms of local gauge-invariant variables. This method reproduces the known solution of the two-dimensional SU (N) theory. In more than two dimensions the action splits into a topological part and a part proportional to αs. We demonstrate the procedure for SU (2) in three dimensions where we reproduce a gravitylike theory. We discuss the four-dimensional case as well. We use a cubic expression in the fields as a space-time metric to obtain a covariant Lagrangian. We also show how the four-dimensional SU (2) theory can be expressed in terms of a local action with six degrees of freedom only.

Interacting D=10 supersymmetric Yang-Mills Theory can be conjugated into a free field theory

1989 ◽  
Vol 231 (1-2) ◽  
pp. 75-79
Author(s):  
Esko Keski-Vakkuri ◽  
Antti J Niemi
Keyword(s):  
Field Theory ◽  
Free Field ◽  
Yang Mills

U(1) Gauge Theory as a Collective Field Theory for Hubbard Model

1988 ◽  
Vol 02 (05) ◽  
pp. 613-623 ◽  
Author(s):  
Tetsuo Matsui
Keyword(s):  
Field Theory ◽  
Hubbard Model ◽  
Gauge Field ◽  
Landau Theory ◽  
Ginzburg Landau ◽  
Gauge Invariant ◽  
High Tc ◽  
Invariant Order ◽  
Path Integral Method ◽  
Higgs Scalar

I construct a collective field theory for Hubbard model of high Tc superconductivity, using a path-integral method in the third quantized (slave boson) form. It is a U(1) gauge invariant theory consisting of a U(1) gauge field and a Higgs scalar. The gauge field stands for resonating valence bonds and describes a (short range) antiferro-paramagnet phase transition by a condensation machanism. The Higgs scalar represents spinless holes carrying electric charges. Through the confining gauge force, there formed bounded hole pairs on each link, which correspond to the vector mesons in lattice QCD. A superconducting phase is to be described by a condensation of a gauge invariant order parameter for these hole pairs, and to be compared with the color confining chirally broken phase in QCD. A Ginzburg-Landau theory for the vector hole-pair field is proposed.

scholarly journals CONNECTING GREEN FUNCTIONS IN AN ARBITRARY PAIR OF GAUGES AND AN APPLICATION TO PLANAR GAUGES

2001 ◽  
Vol 16 (31) ◽  
pp. 5043-5059 ◽  
Author(s):  
SATISH D. JOGLEKAR
Keyword(s):  
Green Function ◽  
Finite Field ◽  
Path Integrals ◽  
Green Functions ◽  
Expectation Values ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Field Dependent ◽  
Gauge Connection ◽  
Arbitrary Gauge

We establish a finite field-dependent BRS transformation that connects the Yang–Mills path integrals with the Faddeev–Popov effective actions for an arbitrary pair of gauges F and F'. We establish a result that relates an arbitrary Green function (either a primary one or that of an operator) in an arbitrary gauge F' to those in gauge F that are compatible to the ones in gauge Fby its construction. This is because the construction preserves expectation values of gauge-invariant observables. We establish parallel results also for the planar gauge-Lorentz gauge connection.

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