UNIFICATION OF GRAVITY, GAUGE AND HIGGS FIELDS BY CONFINED QUANTUM FIELDS II-EFFECTIVE THEORY

1993 ◽  
Vol 08 (10) ◽  
pp. 947-960 ◽  
Author(s):  
TOSHIKI ISSE
Keyword(s):  
Flat Space ◽  
Low Energy ◽  
Effective Theory ◽  
Gauge Fields ◽  
Quantum Fields ◽  
Yang Mills ◽  
Free Fields ◽  
Higgs Fields

Dynamics of quantized free fields (of spin 0 and 1/2) contained in a subspace V* of an (N+4)-dimensional flat space V is studied. The space V* is considered as a neighborhood of a four-dimensional submanifold M arbitrarily embedded into V. We show that Einstein SO (N)-Yang-Mills Higgs theory is induced as a low energy effective theory of the system. Gravity, SO (N) gauge fields and Higgs fields are obtained from embedding functions of M.

UNIFICATION OF GRAVITY, GAUGE AND HIGGS FIELDS BY CONFINED QUANTUM FIELDS – MATHEMATICAL FORMULATION

1993 ◽  
Vol 08 (09) ◽  
pp. 837-849 ◽  
Author(s):  
TOSHIKI ISSE
Keyword(s):  
Simple Model ◽  
Infinite Number ◽  
Mathematical Formulation ◽  
Extrinsic Curvature ◽  
Flat Space ◽  
Gauge Fields ◽  
Unified Theory ◽  
Normal Connection ◽  
Free Fields ◽  
Higgs Fields

Dynamics of quantized free fields (of spin 0 and 1/2) contained in a subspace V* of an (N+4)-dimensional flat space V is studied. The space V* is considered as a neighborhood of a four-dimensional submanifold M arbitrarily embedded into V. We study the system as a simple model of unified theory of gravity (g), SO (N) gauge fields (A) and Higgs fields (ɸ). In this paper classical treatment of the system is given. We show that, especially when the fields have spin 1/2, the system is described by an infinite number of fields in interacting with g, A and ɸ. The fields g, A and ɸ are induced themselves by embedding functions of M and correspond respectively to induced metric, normal connection and extrinsic curvature of M.

Free Quantum Fields

2020 ◽  
pp. 247-260
Author(s):  
Daniel Canarutto
Keyword(s):  
Free Field ◽  
Gauge Fields ◽  
Quantum Field ◽  
Quantum Fields ◽  
Dirac Fields ◽  
Free Fields ◽  
Explicit Expressions

The notion of free quantum field is thoroughly discussed in the linearised setting associated with the choice of a detector. The discussion requires attention to certain details that are often overlooked in the standard literature. Explicit expressions for generic fields, Dirac fields, gauge fields and ghost fields are laid down, as well the ensuing free-field expressions of important functionals. The relations between super-commutators of free fields and propagators, and the canonical super-commutation rules, follow from the above results.

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 Renormalizable Abelian-Projected Effective Gauge Theory Derived from Quantum Chromodynamics II

2003 ◽  
Vol 18 (20) ◽  
pp. 1403-1412 ◽  
Author(s):  
Toru Shinohara
Keyword(s):  
Gauge Theory ◽  
Tensor Field ◽  
Anomalous Dimension ◽  
Low Energy ◽  
Effective Theory ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Antisymmetric Tensor Field ◽  
Group Functions ◽  
Multiplicative Renormalizability

In the previous paper,1 we derived the Abelian projected effective gauge theory as a low energy effective theory of the SU (N) Yang–Mills theory by adopting the maximal Abelian gauge. At that time, we have demonstrated the multiplicative renormalizability of the propagators for the diagonal gluon and the dual Abelian antisymmetric tensor field. In this paper, we show the multiplicative renormalizability of the Green's functions also for the off-diagonal gluon. Moreover, we complement the previous results by calculating the anomalous dimension and the renormalization group functions which are undetermined in the previous paper.

scholarly journals HOPF SOLITON SOLUTIONS FROM LOW ENERGY EFFECTIVE ACTION OF SU(2) YANG–MILLS THEORY

2006 ◽  
Vol 21 (15) ◽  
pp. 1189-1202 ◽  
Author(s):  
NOBUYUKI SAWADO ◽  
NORIKO SHIIKI ◽  
SHINGO TANAKA
Keyword(s):  
Fourth Order ◽  
Effective Action ◽  
Dimensional Space ◽  
Soliton Solutions ◽  
Low Energy ◽  
Effective Theory ◽  
Second Derivative ◽  
Yang Mills ◽  
Extended Action ◽  
Derivative Term

The Skyrme–Faddeev–Niemi (SFN) model which is an O(3) σ-model in three-dimensional space up to fourth-order in the first derivative is regarded as a low-energy effective theory of SU(2) Yang–Mills theory. One can show from the Wilsonian renormalization group argument that the effective action of Yang–Mills theory recovers the SFN in the infrared region. However, the theory contains another fourth-order term which destabilizes soliton solutions. We find the stable soliton solutions in this extended action, introducing a second derivative term as a stabilizer. A perturbative technique for the second derivative term is applied to exclude (or reduce) the ill behavior of the action. A new topological energy bound formula is inferred for the action.

INDEX THEOREM AND CHIRAL ANOMALY IN D = 4, N = 1 SUPERGRAVITY

1990 ◽  
Vol 05 (14) ◽  
pp. 1097-1102 ◽  
Author(s):  
SATOSHI YAJIMA
Keyword(s):  
Index Theorem ◽  
Flat Space ◽  
Integral Approach ◽  
Chiral Anomaly ◽  
Gauge Fields ◽  
Minimal Coupling ◽  
Curved Space ◽  
Yang Mills ◽  
Anomalous Term ◽  
Fermion Fields

The chiral anomaly in D = 4 supergravity coupled to supersymmetric Yang-Mills theory is evaluated by using the path integral approach. We consider not only the minimal coupling between the gravitational and gauge fields and the fermion fields but also the interaction term which mixes the gravitino and gaugino. The explicit form of the new anomalous term is given by rewriting the resultant term obtained in flat space in a form corresponding to curved space.

scholarly journals On genus-one string amplitudes on AdS5 × S5

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Luis F. Alday
Keyword(s):  
Stress Tensor ◽  
Simple Structure ◽  
Strong Coupling Expansion ◽  
Flat Space ◽  
Low Energy ◽  
Yang Mills ◽  
Space Limit ◽  
Type Iib String Theory ◽  
String Amplitudes ◽  
Genus One

Abstract We study non-planar correlators in $$ \mathcal{N} $$ N = 4 super-Yang-Mills in Mellin space. We focus in the stress tensor four-point correlator to order 1/N4 and in a strong coupling expansion. This can be regarded as the genus-one four-point graviton amplitude of type IIB string theory on AdS5× S5 in a low energy expansion. Both the loop supergravity result as well as the tower of stringy corrections have a remarkable simple structure in Mellin space, making manifest important properties such as the correct flat space limit and the structure of UV divergences.

scholarly journals Maximal U(1)Y-violating n-point correlators in $$ \mathcal{N} $$ = 4 super-Yang-Mills theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Michael B. Green ◽  
Congkao Wen
Keyword(s):  
Stress Tensor ◽  
Modular Forms ◽  
Flat Space ◽  
Low Energy ◽  
Superstring Theory ◽  
Recursion Relations ◽  
Yang Mills ◽  
Covariant Derivatives ◽  
Higher Derivative ◽  
Energy Expansion

Abstract This paper concerns a special class of n-point correlation functions of operators in the stress tensor supermultiplet of $$ \mathcal{N} $$ N = 4 supersymmetric SU(N) Yang-Mills theory. These are “maximal U(1)Y-violating” correlators that violate the bonus U(1)Y charge by a maximum of 2(n − 4) units. We will demonstrate that such correlators satisfy SL(2, ℤ)-covariant recursion relations that relate n-point correlators to (n − 1)-point correlators in a manner analogous to the soft dilaton relations that relate the corresponding amplitudes in flat-space type IIB superstring theory. These recursion relations are used to determine terms in the large-N expansion of n-point maximal U(1)Y-violating correlators in the chiral sector, including correlators with four superconformal stress tensor primaries and (n − 4) chiral Lagrangian operators, starting from known properties of the n = 4 case. We concentrate on the first three orders in 1/N beyond the supergravity limit. The Mellin representations of the correlators are polynomials in Mellin variables, which correspond to higher derivative contact terms in the low-energy expansion of type IIB superstring theory in AdS5× S5 at the same orders as R4, d4R4 and d6R4. The coupling constant dependence of these terms is found to be described by non-holomorphic modular forms with holomorphic and anti-holomorphic weights (n − 4, 4 − n) that are SL(2, ℤ)-covariant derivatives of Eisenstein series and certain generalisations. This determines a number of non-leading contributions to U(1)Y-violating n-particle interactions (n > 4) in the low-energy expansion of type IIB superstring amplitudes in AdS5× S5.

scholarly journals The gluon condensate in an effective SU(2) Yang–Mills theory

2019 ◽  
Vol 34 (02) ◽  
pp. 1950018
Author(s):  
A. N. Efremov
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Gluon Condensate ◽  
Energy Scale ◽  
Low Energy ◽  
Effective Theory ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Mexican Hat ◽  
Text Model

We make progress towards a derivation of a low energy effective theory for SU(2) Yang–Mills theory. This low energy action is computed to 1-loop using the renormalization group technique, taking proper care of the Slavnov–Taylor identities in the Maximal Abelian Gauge. After that, we perform the Spin-Charge decomposition in a way proposed by Faddeev and Niemi. The resulting action describes a pair of nonlinear O(3) and [Formula: see text]-models interacting with a scalar field. The potential of the scalar field is a Mexican hat and the location of the minima sets the energy scale of solitonic configurations of the [Formula: see text]-model fields whose excitations correspond to glueball states.

scholarly journals Nonrelativistic fluids on scale covariant Newton–Cartan backgrounds

2017 ◽  
Vol 32 (36) ◽  
pp. 1750206 ◽  
Author(s):  
Arpita Mitra
Keyword(s):  
Berry Phase ◽  
Second Law Of Thermodynamics ◽  
Flat Space ◽  
Low Energy ◽  
Gauge Fields ◽  
Covariant Formalism ◽  
Hydrodynamic Properties ◽  
Scale Invariant ◽  
Ideal Fluids ◽  
Scale Transformations

The nonrelativistic covariant framework for fields is extended to investigate fields and fluids on scale covariant curved backgrounds. The scale covariant Newton–Cartan background is constructed using the localization of space–time symmetries of nonrelativistic fields in flat space. Following this, we provide a Weyl covariant formalism which can be used to study scale invariant fluids. By considering ideal fluids as an example, we describe its thermodynamic and hydrodynamic properties and explicitly demonstrate that it satisfies the local second law of thermodynamics. As a further application, we consider the low energy description of Hall fluids. Specifically, we find that the gauge fields for scale transformations lead to corrections of the Wen–Zee and Berry phase terms contained in the effective action.

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