Analytic continuation for giant gravitons

Abstract

We investigate contributions of giant gravitons to the superconformal index. We concentrate on coincident giant gravitons wrapped around a single cycle, and each contribution is obtained by a certain variable change for fugacities from the index of the worldvolume theory on the giant gravitons. Because we treat the index as a series expansion of the fugacities and the variable change relates different convergence regions, we need an analytic continuation before summing up such contributions. We propose a systematic prescription for the continuation. Although our argument is based on some unproved assumptions, it passes non-trivial numerical checks for some examples. With the prescription we can calculate the indices of the M5-brane theories from those of the M2-brane theories, and vice versa.

Modular factorization of superconformal indices

“…where the floor function is defined as: where s(m, n) is the Dedekind sum defined in (A.8). 48 We also note that for m odd, we can write the second term also in terms of the Dedekind sum: We have not been able to find an explicit formula for f m and f m for general n and ñ, although for any explicit values of (m, n, ñ), its value is obtained by the difference between (D.18) and the first term in (D. 19). We can summarize our formulae.…”

“…See[10] for a review and an extensive collection of early references 2. Further progress aimed at understanding the associated microstates can be found in[13][14][15][16][17][18][19][20][21][22].…”

“…At a more technical level, this can be derived from the contour integral expression of the index by making use of the gauge anomaly cancellation[47] 19. Here we have used invariance Z α v (ρ) under S 13 , a point we will discuss in more detail in Sections 3.2.2 and 3.2.3.…”

Dualities and flavored indices of M2-brane SCFTs

“…• The finite N corrections of the gravity indices of the M2-brane SCFTs describing the M2-branes at the A-type singularity are investigated in [30,[42][43][44]. It would be nice to study the finite N corrections for the other M2-brane SCFTs by further analyzing our flavored indices.…”