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.

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 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.

scholarly journals GAUGE GROUP TQFT AND IMPROVED PERTURBATIVE YANG–MILLS THEORY

1998 ◽  
Vol 13 (06) ◽  
pp. 985-1012 ◽  
Author(s):  
LAURENT BAULIEU ◽  
MARTIN SCHADEN
Keyword(s):  
Gauge Group ◽  
Translational Invariance ◽  
Yang Mills ◽  
Power Corrections ◽  
Topological Quantum ◽  
Gauge Fixing ◽  
Global Zero ◽  
The One ◽  
Definition Of

We reinterpret the Faddeev–Popov gauge-fixing procedure of Yang–Mills theories as the definition of a topological quantum field theory for gauge group elements depending on a background connection. This has the advantage of relating topological gauge-fixing ambiguities to the global breaking of a supersymmetry. The global zero modes of the Faddeev–Popov ghosts are handled in the context of an equivariant cohomology without breaking translational invariance. The gauge-fixing involves constant fields which play the role of moduli and modify the behavior of Green functions at subasymptotic scales. At the one loop level physical implications from these power corrections are gauge invariant.

scholarly journals Celestial superamplitude in $$ \mathcal{N} $$ = 4 SYM theory

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Hongliang Jiang
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Scattering Amplitudes ◽  
Momentum Space ◽  
Ward Identity ◽  
Yang Mills ◽  
Conformal Field ◽  
New Perspective ◽  
Celestial Sphere

Abstract Celestial amplitude is a new reformulation of momentum space scattering amplitudes and offers a promising way for flat holography. In this paper, we study the celestial amplitudes in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills (SYM) theory aiming at understanding the role of superconformal symmetry in celestial holography. We first construct the superconformal generators acting on the celestial superfield which assembles all the on-shell fields in the multiplet together in terms of celestial variables and Grassmann parameters. These generators satisfy the superconformal algebra of $$ \mathcal{N} $$ N = 4 SYM theory. We also compute the three-point and four-point celestial super-amplitudes explicitly. They can be identified as the conformal correlation functions of the celestial superfields living at the celestial sphere. We further study the soft and collinear limits which give rise to the super-Ward identity and super-OPE on the celestial sphere, respectively. Our results initiate a new perspective of understanding the well-studied $$ \mathcal{N} $$ N = 4 SYM amplitudes via 2D celestial conformal field theory.

scholarly journals A REVIEW OF INTEGRABLE DEFORMATIONS IN AdS/CFT

2007 ◽  
Vol 22 (13) ◽  
pp. 915-930 ◽  
Author(s):  
IAN SWANSON
Keyword(s):  
String Theory ◽  
Bethe Ansatz ◽  
Energy Spectra ◽  
Yang Mills ◽  
Twisted String ◽  
Pp Wave ◽  
Integrable Deformations ◽  
Type Iib String Theory ◽  
Bethe Equations ◽  
Wave Limit

Marginal β deformations of [Formula: see text] super-Yang–Mills theory are known to correspond to a certain class of deformations of the S5 background subspace of type IIB string theory in AdS5×S5. An analogous set of deformations of the AdS5 subspace is reviewed here. String energy spectra computed in the near-pp-wave limit of these backgrounds match predictions encoded by discrete, asymptotic Bethe equations, suggesting that the twisted string theory is classically integrable in this regime. These Bethe equations can be derived algorithmically by relying on the existence of Lax representations, and on the Riemann–Hilbert interpretation of the thermodynamic Bethe ansatz. This letter is a review of a seminar given at the Institute for Advanced Study, based on research completed in collaboration with McLoughlin.

scholarly journals EXTENSION OF THE POINCARÉ GROUP AND NON-ABELIAN TENSOR GAUGE FIELDS

2010 ◽  
Vol 25 (31) ◽  
pp. 5765-5785 ◽  
Author(s):  
GEORGE SAVVIDY
Keyword(s):  
Gauge Group ◽  
Gauge Transformation ◽  
Space Time ◽  
Gauge Fields ◽  
Poincaré Group ◽  
Matrix Representations ◽  
Poincare Group ◽  
Yang Mills ◽  
The Matrix ◽  
Transversal Plane

In the recently proposed generalization of the Yang–Mills theory, the group of gauge transformation gets essentially enlarged. This enlargement involves a mixture of the internal and space–time symmetries. The resulting group is an extension of the Poincaré group with infinitely many generators which carry internal and space–time indices. The matrix representations of the extended Poincaré generators are expressible in terms of Pauli–Lubanski vector in one case and in terms of its invariant derivative in another. In the later case the generators of the gauge group are transversal to the momentum and are projecting the non-Abelian tensor gauge fields into the transversal plane, keeping only their positively definite spacelike components.

scholarly journals Surface defects, the superconformal index and q-deformed Yang-Mills

2013 ◽  
Vol 2013 (10) ◽  
Author(s):  
Luis F. Alday ◽  
Mathew Bullimore ◽  
Martin Fluder ◽  
Lotte Hollands
Keyword(s):  
Surface Defects ◽  
Yang Mills ◽  
Superconformal Index

Quantum Tavis–Cummings Model

2019 ◽  
pp. 474-488
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Bethe Ansatz ◽  
Transfer Matrix ◽  
Strong Interaction ◽  
Building Blocks ◽  
Vertex Model ◽  
Algebraic Bethe Ansatz ◽  
Quantum Matter ◽  
Ansatz Approach

This chapter extends the algebraic Bethe ansatz to the quantum Tavis–Cummings model, an N atom generalization of the Jaynes–Cummings model to describe the strong interaction between light and quantum matter. In the case of the quantum Tavis–Cum- mings model there is no underlying vertex model to suggest the constituent building blocks of the algebraic Bethe ansatz approach, e.g.like the L-matrix or ultimately the transfer matrix. The algebraic Bethe ansatz is then first applied to the Tavis–Cummings Hamiltonian with an added Stark term using a conjecture for the transfer matrix. The original Tavis–Cummings model and its algebraic Bethe ansatz are obtained in the limit of vanishing Stark term, which requires considerable care.

scholarly journals New soliton solutions of anti-self-dual Yang-Mills equations

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Masashi Hamanaka ◽  
Shan-Chi Huang
Keyword(s):  
Gauge Group ◽  
Darboux Transformation ◽  
Domain Walls ◽  
Soliton Solutions ◽  
Real Space ◽  
Explicit Calculation ◽  
Yang Mills ◽  
Action Density ◽  
New Type ◽  
Exact Soliton Solutions

Abstract We study exact soliton solutions of anti-self-dual Yang-Mills equations for G = GL(2) in four-dimensional spaces with the Euclidean, Minkowski and Ultrahyperbolic signatures and construct special kinds of one-soliton solutions whose action density TrFμνFμν can be real-valued. These solitons are shown to be new type of domain walls in four dimension by explicit calculation of the real-valued action density. Our results are successful applications of the Darboux transformation developed by Nimmo, Gilson and Ohta. More surprisingly, integration of these action densities over the four-dimensional spaces are suggested to be not infinity but zero. Furthermore, whether gauge group G = U(2) can be realized on our solition solutions or not is also discussed on each real space.

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