Generalized Gradient Flow Equation and Its Application to Super Yang-Mills Theory

We generalize the gradient flow equation for field theories with nonlinearly realized symmetry. Applying the formalism to super Yang-Mills theory, we construct a supersymmetric extension of the gradient flow equation. It can be shown that the super gauge symmetry is preserved in the gradient flow. Furthermore, choosing an appropriate modification term to damp the gauge degrees of freedom, we obtain a gradient flow equation which is closed within the Wess-Zumino gauge.Comment: 35 pages, v2: typos corrected and references added, v3: published versio

Geometries from field theories

We propose a method to define a $d+1$ dimensional geometry from a $d$ dimensional quantum field theory in the $1/N$ expansion. We first construct a $d+1$ dimensional field theory from the $d$ dimensional one via the gradient flow equation, whose flow time $t$ represents the energy scale of the system such that $t\rightarrow 0$ corresponds to the ultra-violet (UV) while $t\rightarrow\infty$ to the infra-red (IR). We then define the induced metric from $d+1$ dimensional field operators. We show that the metric defined in this way becomes classical in the large $N$ limit, in a sense that quantum fluctuations of the metric are suppressed as $1/N$ due to the large $N$ factorization property. As a concrete example, we apply our method to the O(N) non-linear $\sigma$ model in two dimensions. We calculate the three dimensional induced metric, which is shown to describe an AdS space in the massless limit. We finally discuss several open issues in future studies.Comment: 9 pages, the title has been changed, and some contents have also been modified. This version is accepted for a publication in PTE

Flow Equation of N=1 Supersymmetric O(N) Nonlinear Sigma Model in Two Dimensions

We study the flow equation for the $\mathcal{N}=1$ supersymmetric $O(N)$ nonlinear sigma model in two dimensions, which cannot be given by the gradient of the action, as evident from dimensional analysis. Imposing the condition on the flow equation that it respects both the supersymmetry and the $O(N)$ symmetry, we show that the flow equation has a specific form, which however contains an undetermined function of the supersymmetric derivatives $D$ and $\bar D$. Taking the most simple choice, we propose a flow equation for this model. As an application of the flow equation, we give the solution of the equation at the leading order in the large $N$ expansion. The result shows that the flow of the superfield in the model is dominated by the scalar term, since the supersymmetry is unbroken in the original model. It is also shown that the two point function of the superfield is finite at the leading order of the large $N$ expansion.Comment: 17 pages; v2: published versio

Restoration of Lorentz Symmetry for Lifshitz-Type Scalar Theory

The purpose of this paper is to present our study on the restoration of the Lorentz symmetry for a Lifshitz-type scalar theory in the infrared region by using nonperturbative methods. We apply the Wegner-Houghton equation, which is one of the exact renormalization group equations, to the Lifshitz-type theory. Analyzing the equation for a z=2, d=3+1 Lifshitz-type scalar model, and using some variable transformations, we found that broken symmetry terms vanish in the infrared region. This shows that the Lifshitz-type scalar model dynamically restores the Lorentz symmetry at low energy. Our result provides a definition of ultraviolet complete renormalizable scalar field theories. These theories can have nontrivial interaction terms of \phi^{n} (n=4, 6, 8, 10) even when the Lorentz symmetry is restored at low energy.Comment: 24 pages, 7 figures; v2: minor corrections, added references; v3: added comments on the initial conditions in section 4, typos corrected, published versio

Perturbative analysis of the Wess-Zumino flow

We investigate an interacting supersymmetric gradient flow in the Wess-Zumino model. Thanks to the non-renormalization theorem and an appropriate initial condition, we find that any correlator of flowed fields is ultraviolet finite. This is shown at all orders of the perturbation theory using the power counting theorem for 1PI supergraphs. Since the model does not have the gauge symmetry, the mechanism of realizing the ultraviolet finiteness is quite different from that of the Yang-Mills flow, and this could provide further understanding of the gradient flow approach.Comment: 30 pages, 2 figure

Lipid-membrane-incorporated hydrophobic photochromic molecules prepared by the exchange method using cyclodextrins

It was found that the exchange method for the preparation of lipid-membrane-incorporated guest molecules was applicable not only to fullerenes but also to other hydrophobic molecules such as azobenzene and stilbene. Advantages of this method are that the long-term stability of lipid-membrane-incorporated azobenzene solution and the maximum ratio of [stilbene]/[lipid] were higher than those prepared by the classical method, which we call the ‘premixing method’. Photoisomerisations of these photochromic guest molecules in the lipid membranes maintained the morphology of liposomes.This file includes Electronic Supplementary Information.This work was supported by JSPS KAKENHI a Grant-in-Aid for Scientific Research (B) (Grant No. 25288037), a Grant-in-Aid for Challenging Exploratory Research (Grant Nos. 24655128 and 25650053) and a Grant-in-Aid for Young Scientists (A) (Grant No. 24681028)