scholarly journals Generators of local supersymmetry transformation from first-class constraints

2012 ◽  
Vol 90 (7) ◽  
pp. 701-705 ◽  
Author(s):  
D.G.C. McKeon
Keyword(s):  
Supersymmetry Transformation ◽  
Spinning Particle ◽  
Gauge Transformations ◽  
Supersymmetric Gauge

We show how the generator of local supersymmetry transformations can be found from fermionic first-class constraints. This is done by adapting the approaches of Henneaux, Teitelboim and Zanelli, and of Castellani that have been used to find the generator of gauge transformations from bosonic first-class constraints. We illustrate how a supersymmetric gauge generator can be found by considering a spinning particle. The invariances that we find are not those presented in the original discussion of the spinning particle.

scholarly journals On the gauge symmetries of the spinning particle

2014 ◽  
Vol 92 (5) ◽  
pp. 411-414
Author(s):  
N. Kiriushcheva ◽  
S.V. Kuzmin ◽  
D.G.C. McKeon
Keyword(s):  
Simple Model ◽  
Gauge Group ◽  
Gauge Transformation ◽  
Group Structure ◽  
Simple Algebra ◽  
Direct Examination ◽  
Spinning Particle ◽  
Gauge Transformations ◽  
Gauge Symmetries ◽  
New Variables

We reconsider the gauge symmetries of the spinning particle by a direct examination of the Lagrangian using a systematic procedure based on the Noether identities. It proves possible to find a set of local bosonic and fermionic gauge transformations that have a simple gauge group structure, which is a true Lie algebra, both for the massless and massive case. This new fermionic gauge transformation of the “position” and “spin” variables in the action decouples from that of the “einbein” and “gravitino”. It is also possible to redefine the fields so that this simple algebra of commutators of the gauge transformations can be derived directly starting from the Lagrangian written in these new variables. We discuss a possible extension of our analysis of this simple model to more complicated cases.

scholarly journals Renormalization and mixing of the Gluino-Glue operator on the lattice

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
M. Costa ◽  
H. Herodotou ◽  
P. Philippides ◽  
H. Panagopoulos
Keyword(s):  
Quantum Correction ◽  
Dimensional Regularization ◽  
Gauge Parameter ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Quantum Numbers ◽  
Mixing Coefficients ◽  
Free Parameters ◽  
Supersymmetric Gauge ◽  
The One

AbstractWe study the mixing of the Gluino-Glue operator in $$\mathcal{N}=1$$ N = 1 Supersymmetric Yang–Mills theory (SYM), both in dimensional regularization and on the lattice. We calculate its renormalization, which is not merely multiplicative, due to the fact that this operator can mix with non-gauge invariant operators of equal or, on the lattice, lower dimension. These operators carry the same quantum numbers under Lorentz transformations and global gauge transformations, and they have the same ghost number. We compute the one-loop quantum correction for the relevant two-point and three-point Green’s functions of the Gluino-Glue operator. This allows us to determine renormalization factors of the operator in the $${\overline{\mathrm{MS}}}$$ MS ¯ scheme, as well as the mixing coefficients for the other operators. To this end our computations are performed using dimensional and lattice regularizations. We employ a standard discretization where gluinos are defined on lattice sites and gluons reside on the links of the lattice; the discretization is based on Wilson’s formulation of non-supersymmetric gauge theories with clover improvement. The number of colors, $$N_c$$ N c , the gauge parameter, $$\beta $$ β , and the clover coefficient, $$c_{\mathrm{SW}}$$ c SW , are left as free parameters.

scholarly journals N=2 SUPERMULTIPLET OF CURRENTS AND ANOMALOUS TRANSFORMATIONS IN SUPERSYMMETRIC GAUGE THEORY

1998 ◽  
Vol 13 (13) ◽  
pp. 1063-1069 ◽  
Author(s):  
H. ITOYAMA ◽  
M. KOIKE ◽  
H. TAKASHINO
Keyword(s):  
Supersymmetric Gauge Theory ◽  
Gauge Theory ◽  
Energy Momentum Tensor ◽  
Central Charge ◽  
Momentum Tensor ◽  
Quantum Mechanical ◽  
Supersymmetry Transformation ◽  
Loop Order ◽  
Yang Mills ◽  
Supersymmetric Gauge

We examine some properties of supermultiplet consisting of the U (1)J current, extended supercurrents, energy–momentum tensor and the central charge in N = 2 supersymmetric Yang–Mills theory. The superconformal improvement requires adding another supermultiplet starting from the U (1)R current. We determine the anomalous (quantum mechanical) supersymmetry transformation associated with the central charge and the energy–momentum tensor to one-loop order. We find nonvanishing fermionic contribution to the central charge.

Poisson Brackets & Angular Momentum

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Generating Functions ◽  
First Integrals ◽  
Lagrangian Mechanics ◽  
Poisson Brackets ◽  
Coordinate Transformations ◽  
Canonical Transformations ◽  
Gauge Transformations ◽  
The Third ◽  
Point Transformations ◽  
Canonical Coordinate

This chapter discusses canonical transformations and gauge transformations and is divided into three sections. In the first section, canonical coordinate transformations are introduced to the reader through generating functions as the extension of point transformations used in Lagrangian mechanics, with the harmonic oscillator being used as an example of a canonical transformation. In the second section, gauge theory is discussed in the canonical framework and compared to the Lagrangian case. Action-angle variables, direct conditions, symplectomorphisms, holomorphic variables, integrable systems and first integrals are examined. The third section looks at infinitesimal canonical transformations resulting from functions on phase space. Ostrogradsky equations in the canonical setting are also detailed.

Integrability: From Statistical Systems to Gauge Theory

2019 ◽  
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Summer School ◽  
Condensed Matter ◽  
Theoretical Physics ◽  
Conformal Field ◽  
The Past ◽  
Background Material ◽  
Supersymmetric Gauge ◽  
Statistical Systems

This volume contains lectures delivered at the Les Houches Summer School ‘Integrability: from statistical systems to gauge theory’ held in June 2016. The School was focussed on applications of integrability to supersymmetric gauge and string theory, a subject of high and increasing interest in the mathematical and theoretical physics communities over the past decade. Relevant background material was also covered, with lecture series introducing the main concepts and techniques relevant to modern approaches to integrability, conformal field theory, scattering amplitudes, and gauge/string duality. The book will be useful not only to those working directly on integrablility in string and guage theories, but also to researchers in related areas of condensed matter physics and statistical mechanics.

scholarly journals Gauge transformations for twisted spectral triples

2018 ◽  
Vol 108 (12) ◽  
pp. 2589-2626 ◽  
Author(s):  
Giovanni Landi ◽  
Pierre Martinetti
Keyword(s):  
Spectral Triples ◽  
Gauge Transformations ◽  
Twisted Spectral Triples

scholarly journals Supersymmetric gauge anomaly with general homotopic paths

2001 ◽  
Vol 596 (1-2) ◽  
pp. 315-347 ◽  
Author(s):  
S.James Gates ◽  
Marcus T. Grisaru ◽  
Marcia E. Knutt ◽  
Silvia Penati ◽  
Hiroshi Suzuki
Keyword(s):  
Supersymmetric Gauge ◽  
Gauge Anomaly

scholarly journals Singular BPS boundary conditions in $$ \mathcal{N} $$ = (2, 2) supersymmetric gauge theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Tadashi Okazaki ◽  
Douglas J. Smith
Keyword(s):  
String Theory ◽  
Boundary Conditions ◽  
Gauge Theories ◽  
Holomorphic Curve ◽  
Two Dimensional ◽  
Supersymmetric Gauge Theories ◽  
Special Lagrangian ◽  
Supersymmetric Gauge ◽  
M Theory

Abstract We derive general BPS boundary conditions in two-dimensional $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories. We analyze the solutions of these boundary conditions, and in particular those that allow the bulk fields to have poles at the boundary. We also present the brane configurations for the half- and quarter-BPS boundary conditions of the $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories in terms of branes in Type IIA string theory. We find that both A-type and B-type brane configurations are lifted to M-theory as a system of M2-branes ending on an M5-brane wrapped on a product of a holomorphic curve in ℂ2 with a special Lagrangian 3-cycle in ℂ3.

scholarly journals Five-brane current algebras in type II string theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Machiko Hatsuda ◽  
Shin Sasaki ◽  
Masaya Yata
Keyword(s):  
Poisson Bracket ◽  
Gauge Field ◽  
The Self ◽  
Dirac Bracket ◽  
Type Ii ◽  
Gauge Transformations ◽  
Transition Rules ◽  
Superstring Theories ◽  
Kaluza Klein ◽  
Current Algebras

Abstract We study the current algebras of the NS5-branes, the Kaluza-Klein (KK) five-branes and the exotic $$ {5}_2^2 $$ 5 2 2 -branes in type IIA/IIB superstring theories. Their worldvolume theories are governed by the six-dimensional $$ \mathcal{N} $$ N = (2, 0) tensor and the $$ \mathcal{N} $$ N = (1, 1) vector multiplets. We show that the current algebras are determined through the S- and T-dualities. The algebras of the $$ \mathcal{N} $$ N = (2, 0) theories are characterized by the Dirac bracket caused by the self-dual gauge field in the five-brane worldvolumes, while those of the $$ \mathcal{N} $$ N = (1, 1) theories are given by the Poisson bracket. By the use of these algebras, we examine extended spaces in terms of tensor coordinates which are the representation of ten-dimensional supersymmetry. We also examine the transition rules of the currents in the type IIA/IIB supersymmetry algebras in ten dimensions. Based on the algebras, we write down the section conditions in the extended spaces and gauge transformations of the supergravity fields.

scholarly journals Twisted 6d (2, 0) SCFTs on a circle

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Zhihao Duan ◽  
Kimyeong Lee ◽  
June Nahmgoong ◽  
Xin Wang
Keyword(s):  
Lie Groups ◽  
Point Of View ◽  
Partition Functions ◽  
Congruence Subgroups ◽  
Gauge Groups ◽  
Simple Lie Groups ◽  
Instanton Contribution ◽  
Elliptic Genera ◽  
Supersymmetric Gauge ◽  
The One

Abstract We study twisted circle compactification of 6d (2, 0) SCFTs to 5d $$ \mathcal{N} $$ N = 2 supersymmetric gauge theories with non-simply-laced gauge groups. We provide two complementary approaches towards the BPS partition functions, reflecting the 5d and 6d point of view respectively. The first is based on the blowup equations for the instanton partition function, from which in particular we determine explicitly the one-instanton contribution for all simple Lie groups. The second is based on the modular bootstrap program, and we propose a novel modular ansatz for the twisted elliptic genera that transform under the congruence subgroups Γ0(N) of SL(2, ℤ). We conjecture a vanishing bound for the refined Gopakumar-Vafa invariants of the genus one fibered Calabi-Yau threefolds, upon which one can determine the twisted elliptic genera recursively. We use our results to obtain the 6d Cardy formulas and find universal behaviour for all simple Lie groups. In addition, the Cardy formulas remain invariant under the twist once the normalization of the compact circle is taken into account.

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