<p>We consider the theory of a higher-derivative (HD) real scalar field <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> coupled to a complex scalar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math>, the coupling of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math> being given by two types, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>λ</mi><mrow><mi>σ</mi><mi>ϕ</mi></mrow></msub><msup><mi>σ</mi><mi>†</mi></msup><mi>σ</mi><msup><mi>ϕ</mi><mn>2</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ξ</mi><mrow><mi>σ</mi><mi>ϕ</mi></mrow></msub><msup><mi>σ</mi><mi>†</mi></msup><mi>σ</mi><msup><mrow><mo stretchy="false">(</mo><msub><mo>∂</mo><mi>μ</mi></msub><mi>ϕ</mi><mo stretchy="false">)</mo></mrow><mn>2</mn></msup></math>. We evaluate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> one-loop corrections <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>δ</mi><mi>V</mi><mo stretchy="false">(</mo><mi>σ</mi><mo stretchy="false">)</mo></math> to the effective potential of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math>, both the contribution from the positive norm part of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> and that from the <i>negative norm part</i> (ghost). We show that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>δ</mi><mi>V</mi><mo stretchy="false">(</mo><msub><mi>σ</mi><mrow><mi>cl</mi></mrow></msub><mo stretchy="false">)</mo></math> at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>σ</mi><mrow><mi>cl</mi></mrow></msub><mo stretchy="false">→</mo><mi>∞</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>σ</mi><mrow><mi>cl</mi></mrow></msub></math> is a classical value of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math>, is positive, implying the stability of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>δ</mi><mi>V</mi><mo stretchy="false">(</mo><msub><mi>σ</mi><mrow><mi>cl</mi></mrow></msub><mo stretchy="false">)</mo></math> by the HD one-loop radiative corrections at high energy.</p>

Japan

Yugo Abe

Takeo Inami

Keisuke Izumi

UV stability of one-loop radiative corrections in higher-derivative scalar field theory

We investigate the consistency between bulk and boundary causalities in static, spherically symmetric, asymptotically anti-de Sitter (AdS) spacetimes. We derive a general formula that provides sufficient conditions for time advance, where bulk propagation arrives earlier than any boundary propagation. As an application, we show that in Reissner-Nordström-anti de Sitter spacetime, no geodesic satisfies the sufficient conditions for time advance even in the super-extremal case. Furthermore, we demonstrate that the Einstein-Euler-Heisenberg theory exhibits time advance when one or a linear combination of the coupling constants is positive and below an upper bound determined by the AdS length scale.

Lei Fu

Daisuke Yoshida

Consistency between bulk and boundary causalities in asymptotically anti-de Sitter spacetimes

We investigate a gedanken experiment to destroy an extremally charged black hole by dropping a test particle, provided that there are multiple <math><mrow><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></math> gauge fields coupled with each other through higher derivative interactions. It is known that the Coulomb repulsion prevents a test particle that would break the extremal condition from falling into an extremal black hole and therefore the black hole cannot be destroyed. We extend this observation to include higher derivative corrections. Although the extremal condition is modified by the higher derivative interactions, we find that the repulsive force induced by the higher derivative couplings is responsible for preventing a test particle that would break the modified extremal condition to reach the event horizon. Thus, we confirm that the weak cosmic censorship conjecture holds for extremally charged black holes even in the presence of higher derivative corrections, as long as the test particle approximation is justified.

Toshifumi Noumi

Gedanken experiments to destroy a black hole by a test particle: Multiply charged black hole with higher derivative corrections

In general asymptotically flat spacetimes, bearing the null geodesics reaching the future null infinity in mind, we propose new concepts, the “dark horizons” (outer dark horizon and inner dark horizon) as generalizations of the photon sphere. They are defined in terms of the structure of escape/capture cones of photons with respect to a unit timelike vector field to capture the motion of light sources. More specifically, considering a two-sphere that represents a set of emission directions of photons, the dark horizons are located at positions where a hemisphere is marginally included in the capture and escape cones, respectively. In addition, our definition succeeds in incorporating relativistic beaming effect. We show that the dark horizon is absent in the Minkowski spacetime, while they exist in spacetimes with black hole(s) under a certain condition. We derive the general properties of the dark horizons in spherically symmetric spacetimes and explicitly calculate the locations of the dark horizons in the Vaidya spacetime and the Kerr spacetime. In particular, in the Kerr spacetime, the outer dark horizon coincides with the shadow observed from infinity on the rotation axis.

Spain

Masaya Amo

Hirotaka Yoshino

Yoshimune Tomikawa

Tetsuya Shiromizu

A generalization of photon sphere based on escape/capture cone

Abstract We show the well-posed variational principle in constraint systems. In a naive procedure of the variational principle with constraints, the proper number of boundary conditions does not match that of physical degrees of freedom , which implies that, even in theories with up to first-order derivatives, the minimal (or extremal) value of the action with the boundary terms is not a solution of the equation of motion in the Dirac procedure of constrained systems. We propose specific and concrete steps to solve this problem. These steps utilize the Hamilton formalism, which allows us to separate the physical degrees of freedom from the constraints. This reveals the physical degrees of freedom that are necessary to be fixed on boundaries, and also enables us to specify the variables to be fixed and the surface terms.

Keigo Shimada

Kyosuke Tomonari

South Korea

Masahide Yamaguchi

Boundary conditions for constraint systems in variational principle

We obtain the matter-graviton scattering amplitude in the gravitational theory of quadratic curvature, which has   <math> <msubsup> <mi>R</mi> <mi>μν</mi> <mn>2</mn> </msubsup> </math>  $$ {R}_{\mu \nu}^2 $$  term in the action. Unitarity bound is not satisfied because of the existence of negative norm states, while an analog of unitarity bound for S-matrix unitarity holds due to the cancelation among the positive norm states and negative norm ones in the unitarity summation in the optical theorem. The violation of unitarity bound is a counter example of Llewellyn Smith’s conjecture on the relation between tree-level unitarity and renormalizability. We have recently proposed a new conjecture that an analog of the unitarity bound for S-matrix unitarity gives the equivalent conditions to those for renormalizability. We show that the gravitational theory of quadratic curvature is a nontrivial example consistent with our conjecture.

High-energy properties of the graviton scattering in quadratic gravity

By applying the recently proposed (3D rank-0   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$ =4 SCFT)/(non-unitary TQFTs) correspondence to S-fold SCFTs, we construct an exotic class of non-unitary TQFTs labelled by an integer k ≥ 3. The SCFTs are obtained by gauging diagonal SU(2) subgroup of T[SU(2)] theory with Chern-Simons level k. We give the explicit expression for modular data, S and T matrices, of the TQFTs. When k = 4m 2 + 4m + 3 with an integer m ≥ 1, the modular data (modulo a decoupled semion) is identical to a non-unitary Haagerup-Izumi modular data. Thus, we give a physical realization of the exotic non-unitary modular data as well as its generalization using an exotic class of SCFTs.

Dongmin Gang

Dongyeob Kim

Generalized non-unitary Haagerup-Izumi modular data from 3D S-fold SCFTs

In this paper we study various dynamical aspects of the AdS/BCFT correspondence in higher dimensions. We study properties of holographic stress energy tensor by analyzing the metric perturbation in the gravity dual. We also calculate the stress energy tensor for a locally excited state on a half plane in a free scalar CFT. Both of them satisfy a reflective boundary condition that is expected for any BCFTs. We also study the behavior of the scalar field perturbation in the AdS/BCFT setup and show that they also show complete reflections. Moreover, we find that the entanglement entropy of a BCFT computed from the AdS/BCFT matched with that calculated from the Island formula, which supports the Island/BCFT correspondence in higher dimensions. Finally we show how we can calculate one point functions in a BCFT in our gravity dual.

Kenta Suzuki

Tadashi Takayanagi

Norihiro Tanahashi

Brane dynamics of holographic BCFTs

Abstract We discuss a field transformation from fields ψ$_{a}$ to other fields ϕ$_{i}$ that involves derivatives, , and derive conditions for this transformation to be invertible, primarily focusing on the simplest case that the transformation maps between a pair of fields and involves up to their first derivatives. General field transformation of this type changes the number of degrees of freedom; hence, for the transformation to be invertible, it must satisfy certain degeneracy conditions so that additional degrees of freedom do not appear. Our derivation of necessary and sufficient conditions for invertible transformation is based on the method of characteristics, which is used to count the number of independent solutions of a given differential equation. As applications of the invertibility conditions, we show some non-trivial examples of the invertible field transformations with derivatives, and also give a rigorous proof that a simple extension of the disformal transformation involving a second derivative of the scalar field is not invertible.

France

Eugeny Babichev

Invertibility conditions for field transformations with derivatives: Toward extensions of disformal transformation with higher derivatives

Abstract We reexamine the Israel-type proof of the uniqueness theorem of the static spacetime outside the photon surface in the Einstein-conformal scalar system. We derive in a systematic fashion a new divergence identity which plays a key role in the proof. Our divergence identity includes three parameters, allowing us to give a new proof of the uniqueness.