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The giant graviton expansion in $AdS_5 \times S^5$
by Giorgos Eleftheriou, Sameer Murthy, Martí Rosselló
Submission summary
| Authors (as registered SciPost users): | Sameer Murthy |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2312.14921v2 (pdf) |
| Date submitted: | 2024-02-20 16:55 |
| Submitted by: | Murthy, Sameer |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
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Abstract
The superconformal index of $\frac12$-BPS states of $N=4$ U(N) super Yang-Mills theory has a known infinite $q$-series expression with successive terms suppressed by $q^N$. We derive a holographic bulk interpretation of this series by evaluating the corresponding functional integral in the dual $AdS_5 \times S^5$. The integral localizes to a product of small fluctuations of the vacuum and of the collective modes of an arbitrary number of giant-gravitons wrapping an $S^3$ of maximal size inside the $S^5$. The quantum mechanics of the small fluctuations of one maximal giant is described by a supersymmetric version of the Landau problem. The quadratic fluctuation determinant reduces to a sum over the supersymmetric ground states, and precisely reproduces the first non-trivial term in the infinite series. Further, we show that the terms corresponding to multiple giants are obtained precisely by the matrix versions of the above super-quantum-mechanics.
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Report
The authors study the index of the half-BPS giant gravitons. While it has been already given in the literature, they propose an alternative derivation from the bulk string theory. They claim that as the effective Lagrangian of the giant gravitons obtained from the D3-brane action can be viewed as the 1d supersymmetric quantum mechanical Lagrangian for the Landau problem describing a particles in a two-dimensional plane with a constant magnetic flux, the index can be evaluated as its Witten index which has contributions from the lowest Landau level. Though the result of the index is already known, their approach would be potentially interesting and useful for experts working on the holographic duality in the context of string theory and supersymmetric gauge theory. However, there are several parts with which I am confused in the draft and I would like the authors to carefully improve.
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