scholarly journals Superconformal index of low-rank gauge theories via the Bethe Ansatz

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Francesco Benini ◽  
Giovanni Rizi
Keyword(s):  
Gauge Group ◽  
Bethe Ansatz ◽  
Gauge Theories ◽  
Low Rank ◽  
Continuous Family ◽  
Yang Mills ◽  
Superconformal Index ◽  
All Solutions ◽  
One To One

Abstract We study the Bethe Ansatz formula for the superconformal index, in the case of 4d $$ \mathcal{N} $$ N = 4 super-Yang-Mills with gauge group SU(N). We observe that not all solutions to the Bethe Ansatz Equations (BAEs) contribute to the index, and thus formulate “reduced BAEs” such that all and only their solutions contribute. We then propose, sharpening a conjecture of Arabi Ardehali et al. [1], that there is a one-to-one correspondence between branches of solutions to the reduced BAEs and vacua of the 4d $$ \mathcal{N} $$ N = 1* theory. We test the proposal in the case of SU(2) and SU(3). In the case of SU(3), we confirm that there is a continuous family of solutions, whose contribution to the index is non-vanishing.

scholarly journals The Bethe-Ansatz approach to the $$ \mathcal{N} $$ = 4 superconformal index at finite rank

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Alfredo González Lezcano ◽  
Junho Hong ◽  
James T. Liu ◽  
Leopoldo A. Pando Zayas
Keyword(s):  
Gauge Group ◽  
Bethe Ansatz ◽  
Finite Rank ◽  
Yang Mills ◽  
Superconformal Index ◽  
Interesting Pattern ◽  
Ansatz Approach ◽  
Standard Solutions

Abstract We investigate the Bethe-Ansatz approach to the superconformal index of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills with SU(N) gauge group in the context of finite rank, N. We explicitly explore the role of the various types of solutions to the Bethe-Ansatz Equations in recovering the exact index for N = 2, 3. We classify the Bethe-Ansatz Equations solutions as standard (corresponding to a freely acting orbifold T2/ℤm× ℤn) and non-standard. For N = 2, we find that the index is fully recovered by standard solutions and displays an interesting pattern of cancellations. However, for N ≥ 3, the standard solutions alone do not suffice to reconstruct the index. We present quantitative arguments in various regimes of fugacities that highlight the challenging role played by the continuous families of non-standard solutions.

NONRENORMALIZATION THEOREMS OF CHIRAL ANOMALIES AND FINITENESS IN SUPERSYMMETRIC YANG-MILLS THEORIES

1986 ◽  
Vol 01 (04) ◽  
pp. 913-942 ◽  
Author(s):  
O. PIGUET ◽  
K. SIBOLD
Keyword(s):  
Perturbation Theory ◽  
Gauge Group ◽  
Gauge Theories ◽  
Space Time ◽  
Supersymmetric Gauge Theories ◽  
Yang Mills ◽  
Supersymmetric Gauge

We prove a generalized nonrenormalization theorem for U(1) axial anomalies in rigid N=1 supersymmetric gauge theories in 4 space-time dimensions. The theorem implies one-loop criteria for β-functions vanishing to all orders of perturbation theory. The criteria are applicable to all N=1 theories with simple gauge group.

scholarly journals ELECTROWEAK THEORY WITH A MINIMAL LENGTH

2011 ◽  
Vol 26 (24) ◽  
pp. 4251-4285 ◽  
Author(s):  
MARTIN KOBER
Keyword(s):  
Standard Model ◽  
Gauge Group ◽  
Gauge Theories ◽  
Generalized Uncertainty Principle ◽  
Z Bosons ◽  
Minimal Length ◽  
Electroweak Theory ◽  
Yang Mills ◽  
Interaction Terms ◽  
The Standard Model

According to the introduction of a minimal length to quantum field theory, which is directly related to a generalized uncertainty principle, the implementation of the gauge principle becomes much more intricated. It has been shown in another paper how gauge theories have to be extended in general, if there is assumed the existence of a minimal length. In this paper this generalization of the description of gauge theories is applied to the case of Yang–Mills theories with gauge group SU(N) to consider especially the application to the electroweak theory as it appears in the Standard Model. The modifications of the lepton-, Higgs- and gauge field sector of the extended Lagrangian of the electroweak theory maintaining local gauge invariance under SU(2)L ⊗ U(1)Y transformations are investigated. There appear additional interaction terms between the leptons or the Higgs particle respectively with the photon and the W- and Z-bosons as well as additional self-interaction terms of these gauge bosons themselves. It is remarkable that in the quark sector where the full gauge group of the Standard Model, SU(3)c ⊗ SU(2)L ⊗ U(1)Y, has to be considered there arise coupling terms between the gluons und the W- and Z-bosons which means that the electroweak theory is not separated from quantum chromodynamics anymore.

scholarly journals Non-perturbative tests of duality cascades in three dimensional supersymmetric gauge theories

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Masazumi Honda ◽  
Naotaka Kubo
Keyword(s):  
Gauge Group ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Simons Theory ◽  
Partition Functions ◽  
Yang Mills ◽  
Supersymmetric Gauge ◽  
Supersymmetric Theories ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract It has been conjectured that duality cascade occurs in the $$ \mathcal{N} $$ N = 3 supersymmetric Yang-Mills Chern-Simons theory with the gauge group U(N)k × U(N + M)−k coupled to two bi-fundamental hypermultiplets. The brane picture suggests that this duality cascade can be generalized to a class of 3d $$ \mathcal{N} $$ N = 3 supersymmetric quiver gauge theories coming from so-called Hanany-Witten type brane configurations. In this paper we perform non-perturbative tests of the duality cascades using supersymmetry localization. We focus on S3 partition functions and prove predictions from the duality cascades. We also discuss that our result can be applied to generate new dualities for more general theories which include less supersymmetric theories and theories without brane constructions.

scholarly journals Sub-leading structures in superconformal indices: subdominant saddles and logarithmic contributions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Alfredo González Lezcano ◽  
Junho Hong ◽  
James T. Liu ◽  
Leopoldo A. Pando Zayas
Keyword(s):  
Saddle Point ◽  
Bethe Ansatz ◽  
Matrix Model ◽  
Simons Theory ◽  
Logarithmic Correction ◽  
Perfect Agreement ◽  
Yang Mills ◽  
Superconformal Index ◽  
Superconformal Theories ◽  
Ansatz Approach

Abstract We systematically study various sub-leading structures in the superconformal index of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory with SU(N) gauge group. We concentrate in the superconformal index description as a matrix model of elliptic gamma functions and in the Bethe-Ansatz presentation. Our saddle-point approximation goes beyond the Cardy-like limit and we uncover various saddles governed by a matrix model corresponding to SU(N) Chern-Simons theory. The dominant saddle, however, leads to perfect agreement with the Bethe-Ansatz approach. We also determine the logarithmic correction to the superconformal index to be log N, finding precise agreement between the saddle-point and Bethe-Ansatz approaches in their respective approximations. We generalize the two approaches to cover a large class of 4d $$ \mathcal{N} $$ N = 1 superconformal theories. We find that also in this case both approximations agree all the way down to a universal contribution of the form log N. The universality of this last result constitutes a robust signature of this ultraviolet description of asymptotically AdS5 black holes and could be tested by low-energy IIB supergravity.

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 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 Two-loop rational terms in Yang-Mills theories

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Jean-Nicolas Lang ◽  
Stefano Pozzorini ◽  
Hantian Zhang ◽  
Max F. Zoller
Keyword(s):  
Scattering Amplitudes ◽  
Gauge Theories ◽  
A Posteriori ◽  
Four Dimensions ◽  
Yang Mills ◽  
General Properties ◽  
Finite Set ◽  
Numerical Tools ◽  
Loop Amplitudes

Abstract Scattering amplitudes in D dimensions involve particular terms that originate from the interplay of UV poles with the (D − 4)-dimensional parts of loop numerators. Such contributions can be controlled through a finite set of process-independent rational counterterms, which make it possible to compute loop amplitudes with numerical tools that construct the loop numerators in four dimensions. Building on a recent study [1] of the general properties of two-loop rational counterterms, in this paper we investigate their dependence on the choice of renormalisation scheme. We identify a nontrivial form of scheme dependence, which originates from the interplay of mass and field renormalisation with the (D−4)-dimensional parts of loop numerators, and we show that it can be controlled through a new kind of one-loop counterterms. This guarantees that the two-loop rational counterterms for a given renormalisable theory can be derived once and for all in terms of generic renormalisation constants, which can be adapted a posteriori to any scheme. Using this approach, we present the first calculation of the full set of two-loop rational counterterms in Yang-Mills theories. The results are applicable to SU(N) and U(1) gauge theories coupled to nf fermions with arbitrary masses.

scholarly journals Local G2-manifolds, Higgs bundles and a colored quantum mechanics

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Max Hübner
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theories ◽  
Supersymmetric Quantum Mechanics ◽  
Higgs Bundle ◽  
Higgs Bundles ◽  
View Point ◽  
Yang Mills ◽  
G2 Manifolds ◽  
Supersymmetric Gauge ◽  
M Theory

Abstract M-theory on local G2-manifolds engineers 4d minimally supersymmetric gauge theories. We consider ALE-fibered G2-manifolds and study the 4d physics from the view point of a partially twisted 7d supersymmetric Yang-Mills theory and its Higgs bundle. Euclidean M2-brane instantons descend to non-perturbative effects of the 7d supersymmetric Yang-Mills theory, which are found to be in one to one correspondence with the instantons of a colored supersymmetric quantum mechanics. We compute the contributions of M2-brane instantons to the 4d superpotential in the effective 7d description via localization in the colored quantum mechanics. Further we consider non-split Higgs bundles and analyze their 4d spectrum.

scholarly journals CONFORMAL HOUSE

2010 ◽  
Vol 25 (24) ◽  
pp. 4603-4621 ◽  
Author(s):  
THOMAS A. RYTTOV ◽  
FRANCESCO SANNINO
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Gauge Group ◽  
Gauge Theories ◽  
Simultaneous Presence ◽  
Consistency Check ◽  
Effective Lagrangian ◽  
Anomalous Dimensions ◽  
Mass Terms

We investigate the gauge dynamics of nonsupersymmetric SU (N) gauge theories featuring the simultaneous presence of fermionic matter transforming according to two distinct representations of the underlying gauge group. We bound the regions of flavors and colors which can yield a physical infrared fixed point. As a consistency check we recover the previously investigated bounds of the conformal windows when restricting to a single matter representation. The earlier conformal windows can be imagined to be part now of the new conformal house. We predict the nonperturbative anomalous dimensions at the infrared fixed points. We further investigate the effects of adding mass terms to the condensates on the conformal house chiral dynamics and construct the simplest instanton induced effective Lagrangian terms.

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