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

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 forN= 2,3. We classify the Bethe-Ansatz Equations solutions as standard (corresponding to a freely acting orbifoldT²/Z_m×Z_n) and non-standard. ForN= 2, we find that the index is fully recovered by standard solutions and displays an interesting pattern of cancellations. However, forN ≥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.

Authors:

Lezcano, Alfredo González  ^[1];

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• Search DOE PAGES for ORCID "0000-0001-9597-7663"

Hong, Junho ^[2]; Liu, James T.  ^[2];

• Search DOE PAGES for author "Liu, James T."
• Search DOE PAGES for ORCID "0000-0002-9431-7126"

Pando Zayas, Leopoldo A.  ^[3]

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• Search DOE PAGES for ORCID "0000-0003-0727-5958"

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+ Show Author Affiliations

1. The Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); SISSA International School for Advanced Studies and INFN, Trieste (Italy); Universidad de Pinar del Río, Pinar del Rio (Cuba)
2. Univ. of Michigan, Ann Arbor, MI (United States)
3. The Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Univ. of Michigan, Ann Arbor, MI (United States)

Publication Date:

Mon Jun 21 00:00:00 EDT 2021

Research Org.:

Univ. of Michigan, Ann Arbor, MI (United States)

Sponsoring Org.:

USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:

1864652

Alternate Identifier(s):

OSTI ID: 1851003

Grant/Contract Number:  

SC0007859

Resource Type:

Accepted Manuscript

Journal Name:

Journal of High Energy Physics (Online)

Additional Journal Information:

Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2021; Journal Issue: 6; Journal ID: ISSN 1029-8479

Publisher:

Springer Nature

Country of Publication:

United States

Language:

English

Subject:

79 ASTRONOMY AND ASTROPHYSICS; Supersymmetric Gauge Theory; AdS-CFT Correspondence; Black Holes in String Theory; Physics