We propose a new generalization of the Yang-Baxter equation, where the
R-matrix depends on cluster -variables in addition to the spectral
parameters. We point out that we can construct solutions to this new equation
from the recently-found corr...
Journal of Physics A: Mathematical and Theoretical 51(5) 053002 Oct 2016 [Refereed]
We discuss a discretization of the quantum Toda field theory associated with
a semisimple finite-dimensional Lie algebra or a tamely-laced
infinite-dimensional Kac-Moody algebra , generalizing the previous
construction of discrete quantum Liouv...
We point out that the determinant formula for a parabolic Verma module plays
a key role in the study of (super)conformal field theories and in particular
their (super)conformal blocks. The determinant formula is known from the old
work of Jantzen ...
We point out that the determinant formula for a parabolic Verma module plays a key role in the study of (super)conformal field theories and in particular their (super)conformal blocks. The determinant formula is known from the old work of Jantzen ...
We introduce a class of new integrable lattice models labeled by a pair of
positive integers N and r. The integrable model is obtained from the Gauge/YBE
correspondence, which states the equivalence of the 4d N=1 S^1 \times S^3/Z_r
index of a larg...
We propose a new concept of entanglement for quantum systems: entanglement in
theory space. This is defined by decomposing a theory into two by an un-gauging
procedure. We provide two examples where this newly-introduced entanglement is
closely re...
We study 4d superconformal indices for a large class of N=1 superconformal
quiver gauge theories realized combinatorially as a bipartite graph or a set of
"zig-zag paths" on a two-dimensional torus T^2. An exchange of loops, which we
call a "doubl...
We propose an equivalence of the partition functions of two different 3d gauge theories. On one side of the correspondence we consider the partition function of 3d SL(2,R) Chern-Simons theory on a 3-manifold, obtained as a punctured Riemann surfac...
Publ.Res.Inst.Math.Sci.Kyoto B28:193,2011 Feb 2011
We survey geometrical and especially combinatorial aspects of generalized
Donaldson-Thomas invariants (also called BPS invariants) for toric Calabi-Yau
manifolds, emphasizing the role of plane partitions and their generalizations
in the recently p...
The number of BPS bound states of D-branes on a Calabi-Yau manifold depends on two sets of data, the BPS charges and the stability conditions. For D0 and D2-branes bound to a single D6-brane wrapping a Calabi-Yau 3-fold X, both are naturally relat...
This paper summarizes recent developments in the theory of
Bogomol'nyi-Prasad-Sommerfield (BPS) state counting and the wall crossing
phenomena, emphasizing in particular the role of the statistical mechanical
model of crystal melting. This paper i...
Consider the degeneracies of BPS bound states of one D6 brane wrapping Calabi-Yau X with D0 branes and D2 branes. When we include D4-branes wrapping Lagrangian cycle L in addition, D2-branes can end on them. These give rise to new bound states in ...
We construct an explicit example of a generalized Lie 3-algebra from the
octonions. In combination with the result of arXiv:0807.0808, this gives rise
to a three-dimensional N=2 Chern-Simons-matter theory with exceptional gauge
group G_2 and with ...
Hayashi Hirotaka, Tatar Radu, Toda Yukinobu, Watari Taizan, Yamazaki Masahito
Nucl.Phys. B806 224-299 May 2008 [Refereed]
In order to understand both up-type and down-type Yukawa couplings, F-theory is a better framework than the perturbative Type IIB string theory. The duality between the Heterotic and F-theory is a powerful tool in gaining more insights into F-theo...
We review recent developments in the theory of brane tilings and
four-dimensional N=1 supersymmetric quiver gauge theories. This review consists
of two parts. In part I, we describe foundations of brane tilings, emphasizing
the physical interpreta...
J. Reine. Angew. Math. 680,1-22 1 Mar 2007 [Refereed]
We formulate a conjecture which describes the Fukaya category of an exact Lefschetz fibration defined by a Laurent polynomial in two variables in terms of a pair consisting of a consistent dimer model and a perfect matching on it. We prove this co...
Swampland conjectures are a set of proposed necessary conditions for a
low-energy effective field theory to have a UV completion inside a theory of
quantum gravity. Swampland conjectures have interesting phenomenological
consequences, and converse...
It has recently pointed out that a four-dimensional analog of Chern-Simons
theory provides an elegant framework for understanding integrable models with
spectral parameters. The goal of this short note is to better understand the
relation of this ...
Masahiro Ibe, Masahito Yamazaki, Tsutomu T. Yanagida
Nov 2018
We point out that the swampland conjectures forbidding the presence of stable
de Sitter and non-supersymmetric anti-de Sitter vacua require the presence of a
dynamical axion for the electroweak SU(2) gauge theory. The potential energy of
the elect...
We propose a new bilinear Hirota equation for -functions associated
with the root lattice, that provides a "lens" generalisation of the -functions for the elliptic discrete Painlevé equation. Our equations
are characterized by ...
We discuss phenomenological consequences of the recently-introduced
refinements of the de Sitter swampland conjecture. The conjecture constraints
the first and the second derivatives of the scalar potential in terms of two constants and...
