Recent developments in string theory and M theory reveal interesting aspects of some strongly coupled CFTs. As one of the examples, we study the five dimensional $T_N$ CFT compactified on $S^1$, which is realized on the multi-junction of 5-branes introduced by Benini, Benvenuti and Tachikawa. For $N=3$, we explicitly show that the Seiberg-Witten curve agrees with what was previously known in the context of E-string theory.We also discuss the application of our results to the topological string theory and to the two dimensional CFT.
We consider the entropy of higher spin black holes in 2+1 dimensions using the conical singularity approach. By introducing a conical singularity along a non contractible cycle and carefully evaluating its contribution to the Chern Simons action, we derive a simple expression for the entropy of a general stationary higher spin black hole. The resulting formula is shown to satisfy the first law of thermodynamics, and yields agreement with previous results based on integrating the first law. (arXiv:1302.1583 [hep-th])
Causal Dynamical Triangulations (CDT) is a lattice theory where aspects of quantum gravity can be studied. Two-dimensional CDT can be solved analytically and the continuum (quantum) Hamiltonian obtained. We show that this continuum Hamiltonian is the one obtained by quantizing two-dimensional projectable Horava-Lifshitz gravity. (hep-th/1302.6359)
We provide an M-theory geometric set-up to describe four-dimensional N=1
gauge theories. This is realized by a generalization of Hitchin's
equation. This framework encompasses a rich class of theories including
superconformal and confining ones. We show how the spectral curve of the
generalized Hitchin's system encodes the infrared properties of N=1
gauge theory obtained by a superpotential deformation of N=2 class S
theory. The spectral curve consists of a set of equations: one is the
N=2 Seiberg-Witten curve and one is the "N=1 curve", and their
combination gives the Dijkgraaf-Vafa curve when the theory has a
Lagrangian description. This talk is based on
arXiv:1303.0836,
arXiv:1305.5250, and
arXiv:1307.7703.
We present how to make exploit the q-Virasoro block to check the conjectured equality between the parafermion block and the instanton sum on ALE space to a given order. Assuming the K-theoretic lift of the AGT conjecture to hold, which leads to the 2d-4d dictionary of the parameters through the $\beta$ deformed matrix model, we are able to generate the integral representation of the parafermion block.
We analyze the instanton sectors in the very strongly coupled large-$N$ limit ($N\to\infty$ with $g^2$ fixed), where the instanton effect remains finite. By using the exact formula for the partition function of ${\cal N}=2^*$ gauge theories as a solid example,we demonstrate that the instanton sectors in the very strongly coupled large-$N$ limit are related to the ones in the 't Hooft limit ($N\to\infty$ with $g^2N$ fixed) through a simple analytic continuation.We further demonstrate the equivalence between instanton partition functions of two theories related by an orbifold projection. This opens up a new way to exactly analyze the partition functions of low/non supersymmetric theories.
一般化された$\Omega$-background上の$\mathcal{N}=4$ Super Yang-Mills Theoryにおいて超対称性が残る条件を考える。SU(4) R-symmetry Wilson lineを導入してパラメーターをうまく調節することにより、topological twistした時のscalarとtensorの1成分に対応するsuperchargeが保存されるようにすることができる。$\mathcal{N}=4$ Super Yang-Mills Theoryでは3つの独立なtopological twistを考えることができ、以前の研究において各々のtwistについて生き残っているSUSY変換をon-shellで調べた。今回は特にscalar superchargeに着目して、その変換則をoff-shellに拡張し具体的に構成した。作用は各々のtwistに対応するscalar superchargeに対してexactに書くことができ、それぞれ異なるtopological field theoryが構成できることも示した。
Boltzmann equation describes the time development of the velocity distribution in the continuum fluid matter. We formulate the equation using the field theory where the {\it velocity-field} plays the central role. The matter (constituent particles) fields appear as the density and the viscosity. {\it Fluctuation} is examined, and is clearly discriminated from the quantum effect. The time variable is {\it emergently} introduced through the computational process step. The collision term, for the (velocity)**4 potential (4-body interaction), is explicitly obtained and the (statistical) fluctuation is closely explained. The present field theory model does {\it not} conserve energy and is an open-system model. (One dimensional) Navier-Stokes equation , Burger's equation, appears. In the latter part, we present a way to directly define the distribution function by use of the geometry, appearing in the mechanical dynamics, and the Feynman's path-integral. (arXiv:1303.6616)
In March 2013 the Planck team announced its first
cosmological results based on its characterization of the primordial
temperature anisotropies of the microwave sky.
I will review these results focusing particularly
on the implication for fundamental physics. I will also review
forthcoming CMB experiments, particularly those searching from
B modes that would be the tell-tale sign of primordial gravitational
waves generated during inflation.
On the de Sitter background, some modes of gravity contain the scale invariant spectrum which is dominant at the super-horizon scale. It indicates that the corresponding propagator has a logarithmic time dependence which breaks the de Sitter symmetry. We investigate physical effects of soft gravitons on the local dynamics of matter fields at thesub-horizon scale. We show that the infra-red logarithms do not spoil the effective Lorentz invariance in scalar, Dirac and gauge fields. The leading infra-red logarithms can be absorbed by time dependent wave function renormalization factors in these cases. In the interacting field theories with quartic, Yukawa and gauge interactions, we find that the couplings become time dependent with definite scaling exponents. We argue that the relative scaling exponents of the couplings are gauge invariant and physical as we can use the evolution of a coupling as a physical time. Furthermorewe clarify how the infra-red effects depend on the change of the quantization scheme: different parametrization of the metric and the matter field redefinition. We found that the parametrization dependence of the metric can be compensated by shifting the background metric. As for the matter field redefinition, the specific choice with the effective Lorentzinvariance is singled out by unitarity as the kinetic terms are canonically normalized.
de Rhamらが提唱した非線形massive gravityに触発されて，1計量だけで表されるローレンツ不変な質量項をもつEinstein重力理論や修正重力理論の定式化とその量子化を再検討している。Boulware-Deser(1972)の議論を回避する可能性がある質量項として計量テンソルの行列式だけの関数の無限個の重ね合わのものを調べている。弱場近似の下で，タキオンfreeやゴーストfreeになるかどうか，調べた結果を報告する。これらの質量項が存在する重力理論を量子化するためには，Stueckelberg形式を採用する。ただし，従来の簡便な導入ではなく，Izawaによる場の変数変換に関するBRS処方を使って，対称テンソル場に対するベクトルのStueckelberg場を導入するので，FPゴーストを含む全体理論は従来の簡便なStueckelberg形式とは異なる形式となった。現在，もともとのBRS変換とWeyl不変な修正重力のWeyl変換を含む拡張されたBRS変換が構成できるのか調べている。Stueckelberg場が高階微分を含む部分をどう処理するのか，検討中である。また，この質量項の存在が宇宙論的な解がどう変更するのかについてもされるのか，調べた結果を報告する。最後に，この質量項が５番目の座標と関連付けられるのかについても言及する。
We study linear responses of D0-branes in low frequency region by using gauge/gravity correspondence. The dynamics of the D0-branes is described by Matrix theory with finite temperature, which is dual to a near extremal D0-brane black hole solution. We analyze tensor mode and vector modes of a stress tensor and a Ramond-Ramond (R-R) 1-form current of Matrix theory. Then, we show that if a cut-off surface is close to a horizon of the D0-brane black hole, the linear responses take forms similar to the hydrodynamic stress tensor and current on $S^8$. By taking a Rindler limit, those linear responses become to obey the hydrodynamics exactly, which is consistent with previous works on a Rindler fluid. We also show that if the cut-off surface is far from the horizon, the linear responses do not take the forms of the hydrodynamic stress tensor and current on $S^8$. Especially, we find that the vector modes no longer possess a diffusion pole in low frequency region, which indicates that the linear responses of the D0-branes can not be explained by hydrodynamics. (arXiv:1305.2506)
We study integrable deformations of AdS/CFT by focusing upon three kinds of warped AdS$_3$ geometries, 1) space-like warped AdS$_3$, 2) time-like warped AdS$_3$ and 3) null warped AdS$_3$. There geometries are embedded into type IIB supergravity solutions and are regarded as consistent string backgrounds. By restricting the classical motion of strings on the warped AdS$_3\times$S$^1$ subspace, the Landau-Lifshitz sigma models are derived by taking the first moving limit. The first two warped AdS$_3$ spaces correspond to anisotropic deformations of the $sl(2)$ spin chain and the last one to Jordanian deformations. After taking the continuum limit of the deformed spin chains with coherent states, the resulting theories agree with the Landau-Lifshitz sigma models obtained from the string-theory side. (arXiv:1304.1286 [hep-th])
Berkovitsによって構成されたopen superstring field theoryは無限次までの相互作用項を含んでいる。そのうちで４次以上の高次相互作用項は、例えばsuper-Riemann面のsupermoduliのcoveringのために重要だと考えられるが、これら高次項の役割は詳しく調べられてこなかった。そこで本発表では、(４次以上の相互作用項を含まず、発散の問題を抱えている) Wittenのopen superstring field theoryと比較することで、これら高次相互作用項の果たす役割を明らかにする。特に、Wittenの理論が抱える、散乱振幅やゲージ変換に関わる発散が、高次相互作用の存在によってどのように解決されるのかを説明した上で、Berkovitsの理論がWittenの理論のregularizationを与えていると見なせることを示す。なお、本発表は、名古屋大学の飯森氏、理化学研究所の野海氏、東京大学の大川氏との共同研究に基づくものである。
We study an implication of $p-q$ duality (i.e. T-duality and/or spectral duality) on non-perturbative completion of $(p,q)$ minimal string theory. As a result, we argue that the $p-q$ duality even provides a constraint on non-perturbative (or contour) ambiguity possessed by matrix models. In particular, it prohibits some of meta-stability caused by ghost D-instantons, since the description on the dual side otherwise introduces an irregular contour in matrix models.
Topological string amplitude for toric Calabi-Yau manifold is systematically calculated by using the topological vertex. We extend this formalism to the case with the transverse orbifold space $\mathbb{C}^2/\mathbb{Z}_k$. We will show its construction and applications to $\mathcal{N}=2$ gauge theory, Chern-Simons theory, and so on. This talk is based on a collaboration with M. Taki (RIKEN).