Giant graviton expansion of Schur index and quasimodular forms

M. Beccaria (Università del Salento, Dipartimento di Matematica e Fisica Ennio De Giorgi and I.N.F.N. — sezione di Lecce, Via Arnesano, Lecce, I-73100, Italy) ; A. Cabo-Bizet (Università del Salento, Dipartimento di Matematica e Fisica Ennio De Giorgi and I.N.F.N. — sezione di Lecce, Via Arnesano, Lecce, I-73100, Italy)

The flavored superconformal Schur index of N $$ \mathcal{N} $$ = 4 U(N) SYM has finite N corrections encoded in its giant graviton expansion in terms of D3 branes wrapped in AdS 5 × S 5. The key element of this decomposition is the non-trivial index of the theory living on the wrapped brane system. A remarkable feature of the Schur limit is that the brane index is an analytic continuation of the flavored index of N $$ \mathcal{N} $$ = 4 U(n) SYM, where n is the total brane wrapping number. We exploit recent exact results about the Schur index of N $$ \mathcal{N} $$ = 4 U(N) SYM to evaluate the closed form of the brane indices appearing in the giant graviton expansion. Away from the unflavored limit, they are characterized by quasimodular forms providing exact information at all orders in the index universal fugacity. As an application of these results, we present novel exact expressions for the giant graviton expansion of the unflavored Schur index in a class of four dimensional N $$ \mathcal{N} $$ = 2 theories with equal central charges a = c, i.e. the non-Lagrangian theories Γ ̂ SU N $$ \hat{\Gamma}\left(\textrm{SU}(N)\right) $$ with Γ = E 6, E 7, E 8.

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      "source": "Springer", 
      "value": "The flavored superconformal Schur index of   <math> <mi>N</mi> </math>  $$ \\mathcal{N} $$  = 4 U(N) SYM has finite N corrections encoded in its giant graviton expansion in terms of D3 branes wrapped in AdS 5 \u00d7 S 5. The key element of this decomposition is the non-trivial index of the theory living on the wrapped brane system. A remarkable feature of the Schur limit is that the brane index is an analytic continuation of the flavored index of   <math> <mi>N</mi> </math>  $$ \\mathcal{N} $$  = 4 U(n) SYM, where n is the total brane wrapping number. We exploit recent exact results about the Schur index of   <math> <mi>N</mi> </math>  $$ \\mathcal{N} $$  = 4 U(N) SYM to evaluate the closed form of the brane indices appearing in the giant graviton expansion. Away from the unflavored limit, they are characterized by quasimodular forms providing exact information at all orders in the index universal fugacity. As an application of these results, we present novel exact expressions for the giant graviton expansion of the unflavored Schur index in a class of four dimensional   <math> <mi>N</mi> </math>  $$ \\mathcal{N} $$  = 2 theories with equal central charges a = c, i.e. the non-Lagrangian theories   <math> <mover> <mi>\u0393</mi> <mo>\u0302</mo> </mover> <mfenced> <mrow> <mi>SU</mi> <mfenced> <mi>N</mi> </mfenced> </mrow> </mfenced> </math>  $$ \\hat{\\Gamma}\\left(\\textrm{SU}(N)\\right) $$  with \u0393 = E 6, E 7, E 8."
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Published on:
24 May 2024
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2024 (2024)
Issue 5
Pages 1-35
DOI:
https://doi.org/10.1007/JHEP05(2024)282
arXiv:
2403.06509
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: