تقرير
The exact Schur index in closed form
| العنوان: | The exact Schur index in closed form |
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| المؤلفون: | Pan, Yiwen, Peelaers, Wolfger |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics High Energy Physics - Theory Mathematical Physics |
| مصطلحات موضوعية: | High Energy Physics - Theory, Mathematical Physics |
| الوصف: | The Schur limit of the superconformal index of a four-dimensional N = 2 superconformal field theory encodes rich physical information about the protected spectrum of the theory. For a Lagrangian model, this limit of the index can be computed by a contour integral of a multivariate elliptic function. However, surprisingly, so far it has eluded exact evaluation in closed, analytical form. In this paper we propose an elementary approach to bring to heel a large class of these integrals by exploiting the ellipticity of their integrand. Our results take the form of a finite sum of (products of) the well-studied flavored Eisenstein series. In particular, we derive a compact formula for the fully flavored Schur index of all theories of class S of type a1, we put forward a conjecture for the unflavored Schur indices of all N=4 super Yang-Mills theories with gauge group SU(N), and we present closed-form expressions for the index of various other gauge theories of low ranks. We also discuss applications to non-Lagrangian theories, modular properties, and defect indices. Comment: 65 pages; v2: minor clarifications, refs added; v3: typos corrected |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1103/PhysRevD.106.045017 |
| URL الوصول: | http://arxiv.org/abs/2112.09705 |
| رقم الأكسشن: | edsarx.2112.09705 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1103/PhysRevD.106.045017 |
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