We use a recently proposed covariant procedure to reduce the Chern-Simons action of three-dimensional higher-spin gravity to the boundary, resulting in a Lorentz covariant action for higher-order chiral scalars. After gauge-fixing, we obtain a higher-derivative action generalizing the $\textit{s}$ = 1 Floreanini-Jackiw and $\textit{s}$ = 2 Alekseev-Shatashvili actions to arbitrary spin s. For simplicity, we treat the case of general spin at the linearized level, while the full non-linear asymptotic boundary conditions are presented in component form for the SL(3, ℝ) case. Finally, we extend the spin-3 linearized analysis to a background with non-trivial higher-spin charge and show that it has a richer structure of zero modes.

United Kingdom

Taiwan

Calvin Chen

South Korea

Euihun Joung

Karapet Mkrtchyan

Junggi Yoon

Higher-order chiral scalar from boundary reduction of 3d higher-spin gravity

We study the gravitational edge mode in the   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 Jackiw-Teitelboim (JT) supergravity on the disk and its osp(2|1) BF formulation. We revisit the derivation of the finite-temperature Schwarzian action in the conformal gauge of the bosonic JT gravity through wiggling boundary and the frame fluctuation descriptions. Extending our method to   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 JT supergravity, we derive the finite-temperature super-Schwarzian action for the edge mode from both the wiggling boundary and the superframe field fluctuation. We emphasize the crucial role of the inversion of the super-Schwarzian derivative in elucidating the relation between the isometry and the OSp(2|1) gauging of the super-Schwarzian action. In osp(2|1) BF formulation, we discuss the asymptotic AdS condition. We employ the Iwasawa-like decomposition of OSp(2|1) group element to derive the super-Schwarzian action at finite temperature. We demonstrate that the OSp(2|1) gauging arises from inherent redundancy in the Iwasawa-like decomposition. We also discuss the path integral measure obtained from the Haar measure of OSp(2|1).

Kyung-Sun Lee

Akhil Sivakumar

Gravitational edge mode in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 Jackiw-Teitelboim supergravity

We construct the superaction for the <math><mi>T</mi><mover><mi>T</mi><mo>¯</mo></mover></math> deformation of 2D free <math><mi>N</mi><mo>=</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math> supersymmetric model with a deformed superfield. We show that the <math><mi>N</mi><mo>=</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math> off-shell supersymmetry in the free theory is deformed under the <math><mi>T</mi><mover><mi>T</mi><mo>¯</mo></mover></math> deformation, which is incorporated in the deformed superfield. We interpret this superaction as an effective action of the Goldstone superfield for the partial spontaneous breaking of <math><mi>N</mi><mo>=</mo><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math> supersymmetry to <math><mi>N</mi><mo>=</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math>. We show that the unbroken and broken supersymmetry of the effective superaction corresponds to the off-shell <math><mi>N</mi><mo>=</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math> supersymmetry and the off-shell Fermi global nonlinear symmetry in the <math><mi>T</mi><mover><mi>T</mi><mo>¯</mo></mover></math>-deformed theory, respectively. We demonstrate that this effective superaction can be obtained by the nonlinear realization of the partially broken global supersymmetry (PBGS) from the coset superspace. Furthermore, we reproduce the superaction by the constrained superfield method accompanied by a field redefinition.

<math><mi>T</mi><mover><mi>T</mi><mo>¯</mo></mover></math> deformation of <math><mi>N</mi><mo>=</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math> off-shell supersymmetry and partially broken supersymmetry

We study the gravitational edge mode of the Jackiw-Teitelboim (JT) gravity and its sl(2, ℝ) BF theory description with the asymptotic AdS2 boundary condition. We revisit the derivation of the Schwarzian theory from the wiggling boundary as an action for the gravitational edge mode. We present an alternative description for the gravitational edge mode from the metric fluctuation with the fixed boundary, which is often referred as “would-be gauge mode”. We clarify the relation between the wiggling boundary and the would-be gauge mode. We demonstrate a natural top-down derivation of PSL(2, ℝ) gauging and the path integral measure of the Schwarzian theory. In the sl(2, ℝ) BF theory, we incorporate the gravitational edge mode and derive the Schwarzian theory with PSL(2, ℝ) gauging. We also discuss the path integral measure from the Haar measure in the Iwasawa decomposition of PSL(2, ℝ).

India

Prithvi Narayan

Gravitational edge mode in asymptotically AdS2: JT gravity revisited

We study the two-dimensional free symplectic fermion theory with antiperiodic boundary condition. This model has negative norm states with a naive inner product. This negative norm problem can be cured by introducing a new inner product. We demonstrate that this new inner product follows from the connection between the path integral formalism and the operator formalism. This model has a negative central charge, <math><mi>c</mi><mo>=</mo><mo>−</mo><mn>2</mn></math>, and we clarify how two-dimensional conformal field theory with negative central charge can have a non-negative norm. Furthermore, we introduce <math><mi>α</mi></math> vacua in which the Hamiltonian is seemingly non-Hermitian. In spite of non-Hermiticity, we find that the energy spectrum is real. We also compare a correlation function with respect to the <math><mi>α</mi></math> vacua with that of the de Sitter space.

United States

Shinsei Ryu

Unitarity of Symplectic Fermions in <math><mi>α</mi></math> Vacua with Negative Central Charge

We study the boundary effective action of the colored version of the Jackiw-Teitelboim (JT) gravity. We derive the boundary action, which is the color generalization of the Schwarzian action, from the su(N, N) BF formulation of the colored JT gravity. Using different types of the SU(N, N) group decompositions both the zero and finite temperature cases are elaborated. We provide the semi-classical perturbative analysis of the boundary action and discuss the instability of the spin-1 mode and its implication for the quantum chaos. A rainbow-AdS2 geometry is introduced where the color gauge symmetry is spontaneously broken.

Russia

Konstantin Alkalaev

Schwarzian for colored Jackiw-Teitelboim gravity

We introduce the colored version of Jackiw-Teitelboim (JT) gravity which is the two-dimensional dilaton gravity model with matrix-valued fields. It is straightforwardly formulated in terms of BF action with su(N, N) gauge algebra so that the standard JT gravity is embedded as su(1, 1) ⊂ su(N, N) subsector. We also elaborate on the respective metric formulation which is shown to involve the JT fields plus su(N) non-Abelian fields as well as su(N)-matrix valued metric and dilaton fields. Their interactions are governed by minimal couplings and potential terms of cubic and quartic orders involving derivatives.

Color decorations of Jackiw-Teitelboim gravity

We study Python’s lunch geometries in the two-dimensional Jackiw-Teitelboim model coupled to a massless scalar field in the semiclassical limit. We show that all extrema including the minimal quantum extremal surface, bulges and appetizers lie inside the horizon. We obtain fully back-reacted general bulk solutions with a massless scalar field, which can be understood as deformations of black holes. The temperatures of the left/right black holes become in general different from each other. Moreover, in the presence of both state and source deformations at the same time, the asymptotic black hole spacetime is further excited from that of the vacuum solution. We provide information-theoretic interpretation of deformed geometries including Python’s lunches, minimal quantum extremal surface and appetizers according to the entanglement wedge reconstruction hypothesis. By considering the restricted circuit complexity associated with Python’s lunch geometries and the operator complexity of the Petz map reconstructing a code space operation, we show that the observational probability of Python’s lunch degrees of freedom from the boundary is exponentially suppressed. Thus, any bulk causality violation effects related with Python’s lunch degrees are suppressed nonperturbatively.

Dongsu Bak

Chanju Kim

Sang-Heon Yi

Python’s lunches in Jackiw-Teitelboim gravity with matter

We explore the quantum chaos of the coadjoint orbit action of diffeomorphism group of S 1. We study quantum fluctuation around a saddle point to evaluate the soft mode contribution to the out-of-time-ordered correlator. We show that the stability condition of the semi-classical analysis of the coadjoint orbit found in [1] leads to the upper bound on the Lyapunov exponent which is identical to the bound on chaos proven in [2]. The bound is saturated by the coadjoint orbit Diff(S 1)/SL(2) while the other stable orbit Diff(S 1)/U(1) where the SL(2, ℝ) is broken to U(1) has non-maximal Lyapunov exponent.

A bound on chaos from stability

We revisit   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$  deformations of d = 2 theories with fermions with a view toward the quantization. As a simple illustration, we compute the deformed Dirac bracket for a Majorana doublet and confirm the known eigenvalue flows perturbatively. We mostly consider those   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$  theories that can be reconstructed from string-like theories upon integrating out the worldsheet metric. After a quick overview of how this works when we add NSR-like or GS-like fermions, we obtain a known non-supersymmetric   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$  deformation of a   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = (1, 1) theory from the latter, based on the Noether energy-momentum. This world- sheet reconstruction implies that the latter is actually a supersymmetric subsector of a d = 3 GS-like model, implying hidden supercharges, which we do construct explicitly. This brings us to ask about different   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$  deformations, such as manifestly supersymmetric   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$  and also more generally via the symmetric energy-momentum. We show that, for theories with fermions, such choices often lead us to doubling of degrees of freedom, with potential unitarity issues. We show that the extra sector develops a divergent gap in the “small deformation” limit and decouples in the infrared, although it remains uncertain in what sense these can be considered a deformation.