GEOMETRIC FORMULATION OF GAUGE THEORY IN M4×ZN

2000 ◽  
Vol 14 (22n23) ◽  
pp. 2471-2475
Author(s):  
TAKESI SAITO ◽  
KUNIHIKO UEHARA
Keyword(s):  
Gauge Theory ◽  
Noncommutative Geometry ◽  
Point Of View ◽  
Discrete Space ◽  
Yang Mills ◽  
Geometric Point ◽  
Geometric Formulation ◽  
Super Yang Mills Theory

The N=2 Super Yang–Mills theory is reconstructed from a geometric point of view, without employing the entire context of noncommutative geometry in discrete space. This is a revised version of our previous work.

scholarly journals Superfield approach to nilpotent symmetries in 3D Jackiw–Pi model of massive non-Abelian theory

2014 ◽  
Vol 92 (9) ◽  
pp. 1033-1042 ◽  
Author(s):  
S. Gupta ◽  
R. Kumar ◽  
R.P. Malik
Keyword(s):  
Gauge Theory ◽  
Brst Symmetry ◽  
Point Of View ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Abelian Gauge Theory ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Symmetry Transformations ◽  
Augmented Superfield Formalism

In the available literature, only the Becchi–Rouet–Stora–Tyutin (BRST) symmetries are known for the Jackiw–Pi model of the three (2 + 1)-dimensional (3D) massive non-Abelian gauge theory. We derive the off-shell nilpotent [Formula: see text] and absolutely anticommuting (sbsab + sabsb = 0) (anti-)BRST transformations s(a)b corresponding to the usual Yang–Mills gauge transformations of this model by exploiting the “augmented” superfield formalism where the horizontality condition and gauge invariant restrictions blend together in a meaningful manner. There is a non-Yang–Mills (NYM) symmetry in this theory, too. However, we do not touch the NYM symmetry in our present endeavor. This superfield formalism leads to the derivation of an (anti-)BRST invariant Curci–Ferrari restriction, which plays a key role in the proof of absolute anticommutativity of s(a)b. The derivation of the proper anti-BRST symmetry transformations is important from the point of view of geometrical objects called gerbes. A novel feature of our present investigation is the derivation of the (anti-)BRST transformations for the auxiliary field ρ from our superfield formalism, which is neither generated by the (anti-)BRST charges nor obtained from the requirements of nilpotency and (or) absolute anticommutativity of the (anti-)BRST symmetries for our present 3D non-Abelian 1-form gauge theory.

scholarly journals U(1) Lattice Gauge Theory and N=2 Supersymmetric Yang–Mills Theory

1997 ◽  
Vol 12 (35) ◽  
pp. 2665-2681 ◽  
Author(s):  
Jan Ambjørn ◽  
Naoki Sasakura ◽  
Domènec Espriu
Keyword(s):  
Gauge Theory ◽  
Computer Simulations ◽  
Lattice Gauge Theory ◽  
Critical Mass ◽  
Point Of View ◽  
Yang Mills ◽  
Lattice Gauge ◽  
Mass Exponents

We discuss the physics of four-dimensional compact U(1) lattice gauge theory from the point of view of softly broken N=2 supersymmetric SU(2) Yang–Mills theory. We provide arguments in favor of (pseudo-)critical mass exponents 1/3, 5/11 and 1/2, in agreement with the values observed in the computer simulations. We also show that the J CP assignment of some of the lowest lying states can be naturally explained.

scholarly journals EUCLIDEAN SUPER YANG–MILLS THEORY ON A HYPER-KÄHLER EIGHT-FOLD

2005 ◽  
Vol 02 (03) ◽  
pp. 409-424 ◽  
Author(s):  
D. MÜLSCH ◽  
B. GEYER
Keyword(s):  
Gauge Theory ◽  
Theoretical Description ◽  
Yang Mills ◽  
Super Yang Mills Theory

The construction of a NT = 3 cohomological gauge theory on the hyper-Kähler eight-fold, whose group theoretical description was given previously by Blau and Thompson [1], is performed explicitly.

scholarly journals EINSTEIN MANIFOLDS AS YANG–MILLS INSTANTONS

2013 ◽  
Vol 28 (21) ◽  
pp. 1350097 ◽  
Author(s):  
JOHN J. OH ◽  
HYUN SEOK YANG
Keyword(s):  
Gauge Theory ◽  
Einstein Manifold ◽  
Point Of View ◽  
Einstein Equations ◽  
Einstein Manifolds ◽  
Gauge Groups ◽  
Four Dimensions ◽  
Yang Mills ◽  
Theory Point ◽  
The Stability

It is well known that Einstein gravity can be formulated as a gauge theory of Lorentz group where spin connections play a role of gauge fields and Riemann curvature tensors correspond to their field strengths. One can then pose an interesting question: What is the Einstein equation from the gauge theory point of view? Or equivalently, what is the gauge theory object corresponding to Einstein manifolds? We show that the Einstein equations in four dimensions are precisely self-duality equations in Yang–Mills gauge theory and so Einstein manifolds correspond to Yang–Mills instantons in SO (4) = SU (2)L × SU (2)R gauge theory. Specifically, we prove that any Einstein manifold with or without a cosmological constant always arises as the sum of SU (2)L instantons and SU (2)R anti-instantons. This result explains why an Einstein manifold must be stable because two kinds of instantons belong to different gauge groups, instantons in SU (2)L and anti-instantons in SU (2)R, and so they cannot decay into a vacuum. We further illuminate the stability of Einstein manifolds by showing that they carry nontrivial topological invariants.

scholarly journals The superspace representation of super Yang–Mills theory on noncommutative geometry

2018 ◽  
Vol 2018 (4) ◽  
Author(s):  
Masafumi Shimojo ◽  
Satoshi Ishihara ◽  
Hironobu Kataoka ◽  
Atsuko Matsukawa ◽  
Hikaru Sato
Keyword(s):  
Noncommutative Geometry ◽  
Yang Mills ◽  
Super Yang Mills Theory

STRING FIELD THEORY

1987 ◽  
Vol 02 (01) ◽  
pp. 1-76 ◽  
Author(s):  
MICHIO KAKU
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Gauge Theory ◽  
String Field Theory ◽  
Dimensional Space ◽  
Classical Solutions ◽  
Unified Field Theory ◽  
Superstring Theory ◽  
Yang Mills ◽  
Geometric Formulation

String theory has emerged as the leading candidate for a unified field theory of all known forces. However, it is impossible to trust the various phenomenological predictions of superstring theory based on classical solutions alone. It appears that the crucial problem of the theory, breaking ten dimensional space-time down to four dimensions, must be solved nonperturbatively before we can extract reliable predictions. String field theory may be the only formalism in which we can resolve this decisive question. Only a rigorous calculation of the true vacuum of the theory will determine which of the many classical solutions the theory actually predicts. In this review article, we summarize the rapid progress in constructing string field theory actions, such as the development of the covariant BRST theory. We also present the newer geometric formulation of string field theory, from which the BRST theory and the older light cone theory can be derived from first principles. This geometric formulation allows us to derive the complete field theory of strings from two geometric principles, in the same way that general relativity and Yang-Mills theory can be derived from two principles based on global and local symmetry. The geometric formalism therefore reduces string field theory to a problem of finding an invariant under a new local gauge group we call the universal string group (USG). Thus, string field theory is the gauge theory of the universal string group in much the same way that Yang-Mills theory is the gauge theory of SU (N). Thus, the geometric formulation places superstring theory on the same rigorous group theoretical level as general relativity and gauge theory.

scholarly journals GENERALIZED GAUGE THEORIES AND THE WEINBERG–SALAM MODEL WITH DIRAC–KÄHLER FERMIONS

2001 ◽  
Vol 16 (23) ◽  
pp. 3867-3895 ◽  
Author(s):  
NOBORU KAWAMOTO ◽  
HIROSHI UMETSU ◽  
TAKUYA TSUKIOKA
Keyword(s):  
Gauge Theory ◽  
Lie Algebra ◽  
Noncommutative Geometry ◽  
Gauge Theories ◽  
Differential Forms ◽  
Gauge Fields ◽  
Present Formulation ◽  
Yang Mills ◽  
Graded Lie Algebra ◽  
Chern Simons

We extend the previously proposed generalized gauge theory formulation of the Chern–Simons type and topological Yang–Mills type actions into Yang–Mills type actions. We formulate gauge fields and Dirac–Kähler matter fermions by all degrees of differential forms. The simplest version of the model which includes only zero and one-form gauge fields accommodated with the graded Lie algebra of SU (2|1) supergroup leads the Weinberg–Salam model. Thus the Weinberg–Salam model formulated by noncommutative geometry is a particular example of the present formulation.

scholarly journals Super Yang-Mills theories with inhomogeneous mass deformations

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yoonbai Kim ◽  
O-Kab Kwon ◽  
D. D. Tolla
Keyword(s):  
Boundary Condition ◽  
Killing Spinor ◽  
Vacuum Equation ◽  
Constant Mass ◽  
Yang Mills ◽  
Spatial Coordinate ◽  
Mass Functions ◽  
Vacuum Solutions ◽  
Super Yang Mills Theory

Abstract We construct the 4-dimensional $$ \mathcal{N}=\frac{1}{2} $$ N = 1 2 and $$ \mathcal{N} $$ N = 1 inhomogeneously mass-deformed super Yang-Mills theories from the $$ \mathcal{N} $$ N = 1* and $$ \mathcal{N} $$ N = 2* theories, respectively, and analyse their supersymmetric vacua. The inhomogeneity is attributed to the dependence of background fluxes in the type IIB supergravity on a single spatial coordinate. This gives rise to inhomogeneous mass functions in the $$ \mathcal{N} $$ N = 4 super Yang-Mills theory which describes the dynamics of D3-branes. The Killing spinor equations for those inhomogeneous theories lead to the supersymmetric vacuum equation and a boundary condition. We investigate two types of solutions in the $$ \mathcal{N}=\frac{1}{2} $$ N = 1 2 theory, corresponding to the cases of asymptotically constant mass functions and periodic mass functions. For the former case, the boundary condition gives a relation between the parameters of two possibly distinct vacua at the asymptotic boundaries. Brane interpretations for corresponding vacuum solutions in type IIB supergravity are also discussed. For the latter case, we obtain explicit forms of the periodic vacuum solutions.

scholarly journals Exact 1/N expansion of Wilson loop correlators in $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Wolfgang Mück
Keyword(s):  
Matrix Model ◽  
Wilson Loop ◽  
Model Solution ◽  
Wilson Loops ◽  
Combinatorial Formula ◽  
Expectation Value ◽  
Yang Mills ◽  
Hooft Coupling ◽  
The Matrix ◽  
Super Yang Mills Theory

Abstract Supersymmetric circular Wilson loops in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills theory are discussed starting from their Gaussian matrix model representations. Previous results on the generating functions of Wilson loops are reviewed and extended to the more general case of two different loop contours, which is needed to discuss coincident loops with opposite orientations. A combinatorial formula representing the connected correlators of multiply wound Wilson loops in terms of the matrix model solution is derived. Two new results are obtained on the expectation value of the circular Wilson loop, the expansion of which into a series in 1/N and to all orders in the ’t Hooft coupling λ was derived by Drukker and Gross about twenty years ago. The connected correlators of two multiply wound Wilson loops with arbitrary winding numbers are calculated as a series in 1/N. The coefficient functions are derived not only as power series in λ, but also to all orders in λ by expressing them in terms of the coefficients of the Drukker and Gross series. This provides an efficient way to calculate the 1/N series, which can probably be generalized to higher-point correlators.

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