scholarly journals Yangian algebra and correlation functions in planar Gauge theories

2018 ◽  
Vol 5 (2) ◽  
Author(s):  
Niklas Beisert ◽  
Aleksander Garus
Keyword(s):  
Correlation Functions ◽  
Gauge Theories ◽  
Yang Mills ◽  
Local Gauge ◽  
Loop Level ◽  
Gauge Symmetries ◽  
Local Symmetries ◽  
Quantum Anomalies ◽  
Yangian Algebra ◽  
Yangian Symmetry

In this work we consider colour-ordered correlation functions of the fields in integrable planar gauge theories such as \superN=4 supersymmetric Yang–Mills theory with the aim to establish Ward–Takahashi identities corresponding to Yangian symmetries. To this end, we discuss the Yangian algebra relations and discover a novel set of bi-local gauge symmetries for planar gauge theories. We fix the gauge, introduce local and bi-local BRST symmetries and propose Slavnov–Taylor identities corresponding to the various bi-local symmetries. We then verify the validity of these identities for several correlation functions at tree and loop level. Finally, we comment on the possibility of quantum anomalies for Yangian symmetry.

scholarly journals Higgsing towards E-strings

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Joonho Kim ◽  
Seok Kim ◽  
Kimyeong Lee
Keyword(s):  
String Theory ◽  
Gauge Theories ◽  
The Self ◽  
Flavor Symmetry ◽  
Strongly Coupled ◽  
Superconformal Field Theories ◽  
Yang Mills ◽  
Gauge Symmetries ◽  
Elliptic Genera ◽  
Linear Sigma Models

Abstract We explore 6d (1, 0) superconformal field theories with SU(3) and SU(2) gauge symmetries which cascade after Higgsing to the E-string theory on a single M5 near an E8 wall. Specifically, we study the 2d $$ \mathcal{N} $$ N = (0, 4) gauge theories which describe self-dual strings of these 6d theories. The self-dual strings can be also viewed as instanton string solitons of 6d Yang-Mills theories. We find the 2d anomaly-free gauge theories for self-dual strings, amending the naive ADHM gauge theories which are anomalous, and calculate their elliptic genera. While these 2d theories respect the flavor symmetry of each 6d SCFT only partially, their elliptic genera manifest the symmetry fully as these functions as BPS index are invariant in strongly coupled IR limit. Our consistent 2d (0, 4) gauge theories also provide new insights on the non-linear sigma models for the instanton strings, providing novel UV completions of the small instanton singularities. Finally, we construct new 2d quiver gauge theories for the self-dual strings in 6d E-string theory for multiple M5-branes probing the E8 wall, and find their fully refined elliptic genera.

scholarly journals Nilpotent and absolutely anticommuting symmetries in the Freedman–Townsend model: Augmented superfield formalism

2014 ◽  
Vol 29 (31) ◽  
pp. 1450183 ◽  
Author(s):  
A. Shukla ◽  
S. Krishna ◽  
R. P. Malik
Keyword(s):  
Gauge Theories ◽  
Brst Symmetry ◽  
Kinetic Term ◽  
The Novel ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Gauge Symmetries ◽  
Form Field ◽  
Symmetry Transformations ◽  
Augmented Superfield Formalism

We derive the off-shell nilpotent and absolutely anticommuting Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry transformations, corresponding to the (1-form) Yang–Mills (YM) and (2-form) tensorial gauge symmetries of the four (3+1)-dimensional (4D) Freedman–Townsend (FT) model, by exploiting the augmented version of Bonora–Tonin's (BT) superfield approach to BRST formalism where the 4D flat Minkowskian theory is generalized onto the (4, 2)-dimensional supermanifold. One of the novel observations is the fact that we are theoretically compelled to go beyond the horizontality condition (HC) to invoke an additional set of gauge-invariant restrictions (GIRs) for the derivation of the full set of proper (anti-)BRST symmetries. To obtain the (anti-)BRST symmetry transformations, corresponding to the tensorial (2-form) gauge symmetries within the framework of augmented version of BT-superfield approach, we are logically forced to modify the FT-model to incorporate an auxiliary 1-form field and the kinetic term for the antisymmetric (2-form) gauge field. This is also a new observation in our present investigation. We point out some of the key differences between the modified FT-model and Lahiri-model (LM) of the dynamical non-Abelian 2-form gauge theories. We also briefly mention a few similarities.

scholarly journals Charge algebra for non-abelian large gauge symmetries at O(r)

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Miguel Campiglia ◽  
Javier Peraza
Keyword(s):  
Symplectic Structure ◽  
Gauge Theories ◽  
Symmetry Algebra ◽  
Tree Level ◽  
Null Infinity ◽  
Asymptotic Field ◽  
Yang Mills ◽  
Extended Space ◽  
Gauge Symmetries ◽  
Asymptotic Symmetries

Abstract Asymptotic symmetries of gauge theories are known to encode infrared properties of radiative fields. In the context of tree-level Yang-Mills theory, the leading soft behavior of gluons is captured by large gauge symmetries with parameters that are O(1) in the large r expansion towards null infinity. This relation can be extended to subleading order provided one allows for large gauge symmetries with O(r) gauge parameters. The latter, however, violate standard asymptotic field fall-offs and thus their interpretation has remained incomplete. We improve on this situation by presenting a relaxation of the standard asymptotic field behavior that is compatible with O(r) gauge symmetries at linearized level. We show the extended space admits a symplectic structure on which O(1) and O(r) charges are well defined and such that their Poisson brackets reproduce the corresponding symmetry algebra.

scholarly journals ALL SYMMETRIES OF NONEINSTEINIAN GRAVITY IN d=2

1993 ◽  
Vol 08 (08) ◽  
pp. 1383-1397 ◽  
Author(s):  
THOMAS STROBL
Keyword(s):  
Hamiltonian Formulation ◽  
Complete Integrability ◽  
Lorentz Transformations ◽  
Covariant Form ◽  
Field Equations ◽  
Light Cone Gauge ◽  
Gauge Symmetries ◽  
Local Symmetries ◽  
Quantum Anomalies ◽  
Constraint Algebra

The covariant form of the field equations for two-dimensional R2-gravity with torsion as well as its Hamiltonian formulation are shown to suggest the choice of the light-cone gauge. Further a one-to-one correspondence between the Hamiltonian gauge symmetries and the diffeomorphisms and local Lorentz transformations is established, thus proving that there are no hidden local symmetries responsible for the complete integrability of the model. Finally the constraint algebra is shown to have no quantum anomalies so that Dirac’s quantization should be applicable.

Geometry and Quantum Dynamics

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
General Relativity ◽  
Quantum Dynamics ◽  
Gauge Theories ◽  
Brst Symmetry ◽  
Abelian Gauge ◽  
Yang Mills ◽  
History Of ◽  
Brst Invariance

A geometrical derivation of Abelian and non- Abelian gauge theories. The Faddeev–Popov quantisation. BRST invariance and ghost fields. General discussion of BRST symmetry. Application to Yang–Mills theories and general relativity. A brief history of gauge theories.

scholarly journals From correlation functions to event shapes in QCD

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
D. Chicherin ◽  
J. M. Henn ◽  
E. Sokatchev ◽  
K. Yan
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Event Shape ◽  
Proof Of Concept ◽  
Yang Mills ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Event Shapes ◽  
A Charge ◽  
Conserved Currents

Abstract We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community.

scholarly journals Schur correlation functions from q -deformed Yang-Mills theory

2021 ◽  
Vol 103 (10) ◽  
Author(s):  
Yufan Wang ◽  
Yiwen Pan
Keyword(s):  
Correlation Functions ◽  
Yang Mills

scholarly journals Cohomological localization of $$ \mathcal{N} $$ = 2 gauge theories with matter

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Guido Festuccia ◽  
Anastasios Gorantis ◽  
Antonio Pittelli ◽  
Konstantina Polydorou ◽  
Lorenzo Ruggeri
Keyword(s):  
Vector Field ◽  
Extended Supersymmetry ◽  
General Framework ◽  
Gauge Theories ◽  
Killing Vector ◽  
Killing Vector Field ◽  
Explicit Result ◽  
Yang Mills ◽  
Self Duality ◽  
Witten Theory

Abstract We construct a large class of gauge theories with extended supersymmetry on four-dimensional manifolds with a Killing vector field and isolated fixed points. We extend previous results limited to super Yang-Mills theory to general $$ \mathcal{N} $$ N = 2 gauge theories including hypermultiplets. We present a general framework encompassing equivariant Donaldson-Witten theory and Pestun’s theory on S4 as two particular cases. This is achieved by expressing fields in cohomological variables, whose features are dictated by supersymmetry and require a generalized notion of self-duality for two-forms and of chirality for spinors. Finally, we implement localization techniques to compute the exact partition function of the cohomological theories we built up and write the explicit result for manifolds with diverse topologies.

scholarly journals Accidental Gauge Symmetries of Minkowski Spacetime in Teleparallel Theories

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 143
Author(s):  
Jose Beltrán Jiménez ◽  
Tomi S. Koivisto
Keyword(s):  
General Relativity ◽  
Minkowski Spacetime ◽  
Linear Extensions ◽  
Gauge Symmetries ◽  
Linear Spectrum ◽  
Massless Spin ◽  
Non Linear ◽  
Common Framework ◽  
Local Symmetries ◽  
Quadratic Action

In this paper, we provide a general framework for the construction of the Einstein frame within non-linear extensions of the teleparallel equivalents of General Relativity. These include the metric teleparallel and the symmetric teleparallel, but also the general teleparallel theories. We write the actions in a form where we separate the Einstein–Hilbert term, the conformal mode due to the non-linear nature of the theories (which is analogous to the extra degree of freedom in f(R) theories), and the sector that manifestly shows the dynamics arising from the breaking of local symmetries. This frame is then used to study the theories around the Minkowski background, and we show how all the non-linear extensions share the same quadratic action around Minkowski. As a matter of fact, we find that the gauge symmetries that are lost by going to the non-linear generalisations of the teleparallel General Relativity equivalents arise as accidental symmetries in the linear theory around Minkowski. Remarkably, we also find that the conformal mode can be absorbed into a Weyl rescaling of the metric at this order and, consequently, it disappears from the linear spectrum so only the usual massless spin 2 perturbation propagates. These findings unify in a common framework the known fact that no additional modes propagate on Minkowski backgrounds, and we can trace it back to the existence of accidental gauge symmetries of such a background.

scholarly journals Infinite-dimensional fermionic symmetry in supersymmetric gauge theories

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Thomas T. Dumitrescu ◽  
Temple He ◽  
Prahar Mitra ◽  
Andrew Strominger
Keyword(s):  
Ward Identity ◽  
Gauge Theories ◽  
Soft Photon ◽  
Supersymmetric Gauge Theories ◽  
Null Infinity ◽  
Infinite Dimensional ◽  
Charged Matter ◽  
Gauge Symmetries ◽  
Supersymmetric Gauge

Abstract We establish the existence of an infinite-dimensional fermionic symmetry in four-dimensional supersymmetric gauge theories by analyzing semiclassical photino dynamics in abelian $$ \mathcal{N} $$ N = 1 theories with charged matter. The symmetry is parametrized by a spinor-valued function on an asymptotic S2 at null infinity. It is not manifest at the level of the Lagrangian, but acts non-trivially on physical states, and its Ward identity is the soft photino theorem. The infinite-dimensional fermionic symmetry resides in the same $$ \mathcal{N} $$ N = 1 supermultiplet as the physically non-trivial large gauge symmetries associated with the soft photon theorem.

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