<p>We extend the Kac-Moody (KM) boundary conditions of AdS<sub>3</sub> gravity by incorporating fermionic fields. For <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> <mo>=</mo> <mfenced close=")" open="(" separators=","> <mn>1</mn> <mn>1</mn> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N}=\left(1,1\right) \)</EquationSource> </InlineEquation> AdS<sub>3</sub> supergravity, we show that there are two possible ways to implement the fermionic extension. In the first, the extended KM boundary conditions are related to the standard super-Virasoro (VS) boundary conditions through a large gauge transformation realized by the <i>super-Miura map</i> between fields and chemical potentials, establishing a supersymmetric generalization of the KM-VS correspondence. In the second, a more general boundary configuration leads to strong constraints on the fermionic chemical potentials, yet offers a much richer asymptotic structure. It provides us a novel realization of the extended Kac-Moody algebra, and a geometric interpretation in terms of folds in the relativistic free-fermion droplet. Finally, we quantize the latter theory by promoting the classical Poisson brackets to (anti-)commutators, construct the corresponding Hilbert space, and show that the resulting spectrum contains only bosonic soft excitations, with no additional fermionic soft modes.</p>

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Supersymmetric extensions of Kac-Moody boundary conditions in AdS3 gravity

  • Nabamita Banerjee,
  • Vedant Bhutra,
  • Suvankar Dutta,
  • Soumava Kundu

摘要

We extend the Kac-Moody (KM) boundary conditions of AdS3 gravity by incorporating fermionic fields. For N = 1 1 \( \mathcal{N}=\left(1,1\right) \) AdS3 supergravity, we show that there are two possible ways to implement the fermionic extension. In the first, the extended KM boundary conditions are related to the standard super-Virasoro (VS) boundary conditions through a large gauge transformation realized by the super-Miura map between fields and chemical potentials, establishing a supersymmetric generalization of the KM-VS correspondence. In the second, a more general boundary configuration leads to strong constraints on the fermionic chemical potentials, yet offers a much richer asymptotic structure. It provides us a novel realization of the extended Kac-Moody algebra, and a geometric interpretation in terms of folds in the relativistic free-fermion droplet. Finally, we quantize the latter theory by promoting the classical Poisson brackets to (anti-)commutators, construct the corresponding Hilbert space, and show that the resulting spectrum contains only bosonic soft excitations, with no additional fermionic soft modes.