We construct superinvariants in M-theory via local supersymmetry, which include ($\textit{DF}$) terms and fermionic bilinear terms with mass dimension eight. The bases of the ($\textit{DF}$) and the fermionic bilinear terms are classified and the variations under the local supersymmetry are evaluated by using the Mathematica codes. By imposing the local supersymmetry, we find that 24 independent terms of ($\textit{DF}$) are governed by 10 parameters. The result is consistent with the effective action obtained by analyzing scattering amplitudes of superparticles or supermembranes.

Japan

Yoshifumi Hyakutake

Effective action in M-theory: ($\textit{DF}$)

Abstract We investigate the inflationary expansion of the universe induced by higher-curvature corrections in M-theory. The inflationary evolution of the geometry is discussed in K. Hiraga and Y. Hyakutake, Prog. Theor. Exp. Phys. 2018, 113B03 (2018), which we follow to analyze metric perturbations around the background. We especially focus on scalar perturbations and analyze linearized equations of motion for the scalar perturbations. By solving these equations explicitly, we evaluate the power spectrum of the curvature perturbation. The scalar spectrum index is estimated under some assumptions, and we show that it becomes close to 1.

Kazuho Hiraga

Scalar cosmological perturbations in M-theory with higher-derivative corrections

Abstract We investigate inflationary cosmology by solving the effective action of M-theory, which consists of 11-dimensional supergravity and quartic terms of the Weyl tensor. The metric is simply expressed by two scale factors, one for the spatial directions and the other for the internal directions. Since the effective action of M-theory is constructed perturbatively, we also solve the equations of motion perturbatively. We will show that the classical solution of 11-dimensional supergravity does not represent inflationary expansion, but if we include the quantum corrections, the behavior of the solution around the very early time is modified and the inflationary scenario is realized. The inflation naturally ends when the scalar curvature becomes small and quartic terms of the Weyl tensor are negligible.

Inflationary cosmology via quantum corrections in M-theory Planck Collaboration BICEP2/Keck and Planck Collaborations BICEP2 and Keck Array Collaborations

We conjecture fuzzy configurations of D0-branes in the Banks-Fischler-Shenker-Susskind (BFSS) matrix model as microstates of the black hole. Fuzzy configurations of D0-branes consist of localized fuzzy objects in three spatial directions which are smeared into six internal directions. Since the solutions are time dependent, these are non-Bogomol’nyi-Prasad-Sommerfield (non-BPS) configurations and have internal energy compared with static case. Especially, we examine the smeared fuzzy sphere in the BFSS matrix model, which will correspond to the microstate of the charged black hole in four dimensions, and compare the effective potential in that background with the result obtained by the near horizon geometry of the black 0-brane. The qualitative features of two descriptions agree with each other; thus, we expect that the smeared fuzzy sphere corresponds to one of the microstates of the charged black hole. We also examine the smeared fuzzy cylinder which will correspond to the flat space time.

Black hole and fuzzy objects in the BFSS matrix model

One of important directions in superstring theory is to reveal the quantum nature of black hole. In this paper we embed Schwarzschild black hole into superstring theory or M-theory, which we call a smeared black hole, and resolve quantum corrections to it. Furthermore we boost the smeared black hole along the 11th direction and construct a smeared quantum black 0-brane in 10 dimensions. Quantum aspects of the thermodynamic for these black objects are investigated in detail. We also discuss radiations of a string and a D0-brane from the smeared quantum black 0-brane.

Quantum aspects of black objects in string theory

We take into account higher derivative R 4 corrections in M-theory and construct quantum black hole and black string solutions in 11 dimensions up to the next leading order. The quantum black string is stretching along the 11th direction and the Gregory-Laflamme instability is examined at the quantum level. Thermodynamics of the boosted quantum black hole and black string are also discussed. Especially we take the near horizon limit of the quantum black string and investigate its instability quantitatively.

Boosted quantum black hole and black string in M-theory, and quantum correction to Gregory-Laflamme instability

The effective action of superstring theory or M-theory is approximated by supergravity in the low energy limit, and quantum corrections to the supergravity are taken into account by including higher derivative terms. In this paper, we consider equations of motion with those higher derivative terms in M-theory and solve them to derive quantum M-wave solution. A quantum black 0-brane solution is also obtained by Kaluza-Klein dimensional reduction of the M-wave solution. The quantum black 0-brane is asymptotically flat and uniquely determined by imposing appropriate conditions. The mass and the R-R charge of the quantum black 0-brane are derived by using the ADM mass and the charge formulae, and we see that only the mass is affected by the quantum correction. Various limits of the quantum black 0-brane are also considered, and especially we show that an internal energy in the near horizon limit is correctly reproduced.

Quantum M-wave and black 0-brane

We investigate a bunch of D0-branes to reveal their quantum nature from the gravity side. In the classical limit, it is well described by a non-extremal black 0-brane in type IIA supergravity. The solution is uplifted to the eleven dimensions and expressed by a non-extremal M-wave solution. After reviewing the effective action for the M-theory, we explicitly solve the equations of motion for the near-horizon geometry of the M-wave. As a result, we derive a unique solution that includes the effect of the quantum gravity. The thermodynamic properties of the quantum near-horizon geometry of the black 0-brane are also studied by using Wald's entropy formula. Combining our result with that of the Monte Carlo simulation of the dual thermal gauge theory, we find strong evidence for the gauge/gravity duality in the D0-brane system at the level of quantum gravity.