International Journal of Modern Physics A

In quantum gravity or string theory, it is natural to take the topology change of the space into account. We consider the low energy effective action for such case and show that it does not have a simple form of the local action but has a multilocal form. Actually, in quantum gravity or matrix model, there are some mechanisms that the low energy effective action becomes S_eff = ∑_ic_i S_i + ∑_ijc_ijS_iS_j + ∑_ijkc_ijk S_i S_j S_k + ⋯, where S_i is a local action of the form . We further discuss that the topology change of the space naturally leads to the multiverse in which indefinite number of macroscopic universes exist in parallel. In this case, the space–time coordinates x in the multilocal action may sit either in the same universe or in different ones. We then consider the wave function of the entire multiverse, and see how the locality and causality are recovered in such theory. We further discuss the possibility of solving the naturalness problem. In doing so, we need to introduce some assumptions to interpret the multiverse wave function. We consider two different possibilities. One is to simply assume the probabilistic interpretation for the multiverse wave function. The other is to assume infrared cutoff independence of the partition function of the universe. In both cases, we find that the big fix occurs, in which all the coupling constants in the low energy physics are determined by the dynamics of the multiverse. Actually, we find that they are fixed in such a way that the total entropy of the universe at the late stage (in the far future) is maximized. Although the argument here is similar to Coleman's original one given in the late 1980s, our results are based on Lorentzian signature theory and the dynamical mechanism is rather different.

We study the Lorentzian version of the type IIB matrix model as a nonperturbative formulation of superstring theory in (9+1)-dimensions. Monte Carlo results show that not only space but also time emerges dynamically in this model. Furthermore, the real-time dynamics extracted from the matrices turns out to be remarkable: 3 out of 9 spatial directions start to expand at some critical time. This can be interpreted as the birth of our Universe.

We review three topics on the recent application of the AdS/CFT correspondence to hard processes: deep inelastic scattering, e⁺e^- annihilation and jet quenching at finite temperature.

In this paper, we will explain an application of holographic entanglement entropy to Fermi surface physics. These holographic arguments show that Landau–Fermi liquids do not have any gravity duals in the purely classical limit [N. Ogawa, T. Takayanagi and T. Ugajin, J. High Energy Phys.125, 1 (2012), arXiv:1111.1023 [hep-th]].

We outline a comprehensive and first-principle solution to the wall-crossing problem in D = 4N = 2 Seiberg–Witten theories. We start with a brief review of the multi-centered nature of the typical BPS states and of how this allows them to disappear abruptly as parameters or vacuum moduli are continuously changed. This means that the wall-crossing problem is really a bound state formation/dissociation problem. A low energy dynamics for arbitrary collections of dyons is derived, with the proximity to the so-called marginal stability wall playing the role of the small expansion parameter. We discover that the low energy dynamics of such BPS dyons cannot be reduced to one on the classical moduli space, , yet the index can be phrased in terms of . The so-called rational invariant, first seen in Kontsevich–Soibelman formalism of wall-crossing, is shown to incorporate Bose/Fermi statistics automatically. Furthermore, an equivariant version of the index is shown to compute the protected spin character of the underlying D = 4N = 2 theory, where isometry of is identified as a diagonal subgroup of rotation SU(2)_L and R-symmetry SU(2)_R.

We study the local properties of a class of codimension-2 defects of the 6d theories of type J = A, D, E labeled by nilpotent orbits of a Lie algebra , where is determined by J and the outer-automorphism twist around the defect. This class is a natural generalization of the defects of the six-dimensional (6d) theory of type SU(N) labeled by a Young diagram with N boxes. For any of these defects, we determine its contribution to the dimension of the Higgs branch, to the Coulomb branch operators and their scaling dimensions, to the four-dimensional (4d) central charges a and c and to the flavor central charge k.

We propose an explicit construction for the integrable models on Poisson submanifolds of the Lie groups. The integrals of motion are computed in cluster variables via the Lax map. This generalized construction for the co-extended loop groups allows to formulate, in general terms, some new classes of integrable models.

Character expansion expresses extended HOMFLY polynomials through traces of products of finite-dimensional - and Racah mixing matrices. We conjecture that the mixing matrices are expressed entirely in terms of the eigenvalues of the corresponding -matrices. Even a weaker (and, perhaps, more reliable) version of this conjecture is sufficient to explicitly calculate HOMFLY polynomials for all the 3-strand braids in arbitrary (anti)symmetric representations. We list the examples of so obtained polynomials for R = [3] and R = [4], and they are in accordance with the known answers for torus and figure-eight knots, as well as for the colored special and Jones polynomials. This provides an indirect evidence in support of our conjecture.