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

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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.

Section: Jhep05(2024)282 4 Giant-graviton Expansion Of the Index In U...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Giant graviton expansion of Schur index and quasimodular forms

Beccaria,

Cabo-Bizet

2024

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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.

Schur line defect correlators and giant graviton expansion

Beccaria

2024

We consider Schur line defect correlators in four dimensional $$ \mathcal{N} $$ N = 4 U(N) SYM and their giant graviton expansion encoding finite N corrections to the large N limit. We compute in closed form the single giant graviton contribution to correlators with general insertions of $$ \frac{1}{2} $$ 1 2 -BPS charged Wilson lines. For the 2-point function with fundamental and anti-fundamental Wilson lines, we match the result from fluctuations of two half-infinite strings ending on the giant graviton, recently proposed in arXiv:2403.11543. In particular, we prove exact factorization of the defect contribution with respect to wrapped D3 brane fluctuations representing the single giant graviton correction to the undecorated Schur index. This follows from a finite-difference representation of the Schur line defect index in terms of the index without defects, and similar factorization holds quite generally for more complicated defect configurations. In particular, the single giant graviton contribution to the 4-point function with two fundamental and two anti-fundamental lines is computed and discussed in this perspective.