Trace relations and open string vacua

The flavored superconformal Schur index of $$ \mathcal{N} $$ N = 4 U(N) SYM has finite N corrections encoded in its giant graviton expansion in terms of D3 branes wrapped in AdS5 × S5. 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 $$ \mathcal{N} $$ N = 4 U(n) SYM, where n is the total brane wrapping number. We exploit recent exact results about the Schur index of $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ N = 2 theories with equal central charges a = c, i.e. the non-Lagrangian theories $$ \hat{\Gamma}\left(\textrm{SU}(N)\right) $$ Γ ̂ SU N with Γ = E6, E7, E8.

mentioning

confidence: 99%

Giant graviton expansion of Schur index and quasimodular forms

Beccaria,

Cabo-Bizet

2024

Large N Schur index of $$ \mathcal{N} $$ = 4 SYM from semiclassical D3 brane

Beccaria,

Cabo-Bizet

2024

We consider the refined Schur superconformal index of 4d $$ \mathcal{N} $$ N = 4 U(N) SYM and the first term of its giant-graviton expansion, first predicted in arXiv:2001.11667 using indirect superconformal algebra considerations and analytic continuation of fugacities. This correction is the leading non-perturbative correction to the index at large N and we reproduce it from the semiclassical partition function of quantum D3 brane wrapped on S1 × S3 in a twisted modification of the AdS5 × S5 string background, depending on the index R-symmetry fugacity. Our calculation does not exploit directly supersymmetry. It is based on the determination of the partition function of the various bosonic and fermionic fluctuations on the wrapped brane whose action is conformal with specific constant holonomies along thermal cycle. We show how those partition functions may be obtained by adapting the operator counting method of Cardy to the twisted background.

One-loop quantization of Euclidean D3-branes in holographic backgrounds

Gautason,

van Muiden

2024

In this note we analyze the semi-classical quantization of D3-branes in three different holographic backgrounds in type IIB string theory. The first background is Euclidean AdS5 with S1× S3 boundary accompanied with a twist to preserve supersymmetry. We work out the spectrum of fluctuations around the classical D3-brane configuration, compute its one-loop partition function, and match to the non-perturbative correction to the superconformal index of $$ \mathcal{N} $$ N = 4 SYM. We then study Euclidean D3-branes in the Pilch-Warner geometry dual to the IR Leigh-Strassler fixed point of $$ \mathcal{N} $$ N = 1* with the aim to find non-perturbative corrections to its index. Finally we study Euclidean D3-branes in the non-geometric $$ \mathcal{N} $$ N = 2 J-fold background which is dual to the gauging of the 3D Gaiotto-Witten SCFT.