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Giant Gravitons from Holomorphic Surfaces

Andrei Mikhailov

TL;DR

Giant Gravitons from Holomorphic Surfaces develops a unifying framework in which supersymmetric branes wrap holomorphic surfaces inside AdS spacetimes and move along a preferred null direction. The authors show that intersecting holomorphic surfaces with submanifolds like S^5, T^{1,1}, S^7, or S^4, and evolving along the associated e^{||} direction yields BPS configurations with fractions 1/2, 1/4, or 1/8 of preserved supersymmetry across various AdS backgrounds. The work connects these classical solutions to the spectrum of BPS states in the dual CFT and provides detailed spinor analyses to establish supersymmetry, along with energy and angular-momentum relations that saturate the BPS bound. It also explores flat-space analogues, highlighting the generality of moving holomorphic-brane constructions beyond curved backgrounds. The results illuminate how large numbers of BPS states arise as quantum superpositions of giant gravitons, with potential implications for degeneracy counting and AdS/CFT dynamics.

Abstract

We introduce a class of supersymmetric cycles in spacetimes of the form AdS times a sphere or $T^{1,1}$ which can be considered as generalizations of the giant gravitons. Branes wrapped on these cycles preserve $1\over 2$, $1\over 4$ or $1\over 8$ of the supersymmetry. On the CFT side these configurations correspond to superpositions of the large number of BPS states.

Giant Gravitons from Holomorphic Surfaces

TL;DR

Giant Gravitons from Holomorphic Surfaces develops a unifying framework in which supersymmetric branes wrap holomorphic surfaces inside AdS spacetimes and move along a preferred null direction. The authors show that intersecting holomorphic surfaces with submanifolds like S^5, T^{1,1}, S^7, or S^4, and evolving along the associated e^{||} direction yields BPS configurations with fractions 1/2, 1/4, or 1/8 of preserved supersymmetry across various AdS backgrounds. The work connects these classical solutions to the spectrum of BPS states in the dual CFT and provides detailed spinor analyses to establish supersymmetry, along with energy and angular-momentum relations that saturate the BPS bound. It also explores flat-space analogues, highlighting the generality of moving holomorphic-brane constructions beyond curved backgrounds. The results illuminate how large numbers of BPS states arise as quantum superpositions of giant gravitons, with potential implications for degeneracy counting and AdS/CFT dynamics.

Abstract

We introduce a class of supersymmetric cycles in spacetimes of the form AdS times a sphere or which can be considered as generalizations of the giant gravitons. Branes wrapped on these cycles preserve , or of the supersymmetry. On the CFT side these configurations correspond to superpositions of the large number of BPS states.

Paper Structure

This paper contains 20 sections, 75 equations.

Table of Contents

  1. Introduction
  2. The construction
  3. $AdS_5\times S^5$ and $AdS_5\times T^{1,1}$
  4. $AdS_3\times S^3$
  5. Giant gravitons in $AdS_4\times S^7$ and $AdS_7\times S^4$
  6. Giant Gravitons and BPS States
  7. Supersymmetry for $1\over 8$ BPS giant gravitons in $AdS_5\times S^5$
  8. Spinors in $AdS_{p-1}\times S^{q-1}$
  9. Some geometric background
  10. Supersymmetry for $1\over 8$ BPS giant gravitons
  11. Supersymmetry for $1\over 4$ BPS giant gravitons in $AdS_3\times S^3$
  12. $AdS_4\times S^7$ and $AdS_7\times S^4$
  13. Energy and Angular Momentum
  14. Energy of the Giant Graviton
  15. BPS bound
  16. ...and 5 more sections