vol. 92 | iTHES

Vol. 92, August 10th, 2015

• Announcement
• Upcoming Events
• Paper of the week

# Infinite circumference limit of conformal field theory

## From the Office

The office of iTHES assistant, Ms.Chikako Oota is situated at the second floor of the main research building, room # 246. The extension number is 3261. She will be at the office from 10 a.m. to 16 p.m.

## Announcement

iTHES NewsLetter has summer break on Aug.11-30.
The next NewsLetter will be issued on Aug.31.
Have a nice summer !

## Upcoming Events

GRB Workshop 2015 at RIKEN

Date: 31st Aug.- 2nd Sep 2015
Place: Suzuki Umetaro Hall
http://abb-lab.riken.jp/index.php/workshop/grb_workshop_2015/

Joint iTHES - Math. Cooperation Program Symposium

Date: Sep. 2 (Wed.) 10:00am-
Place: Research Organization of Information and Systems
http://rois.ac.jp/english/index.html
Program: TBA
Math. Coop. Program: http://coop-math.ism.ac.jp/

The 6th iTHES Academic-Industrial Innovation Lecture

Date: Oct. 22(Thurs.) 15:00-16:30
Place: TBA
Speaker: Hironori Kokubo (Takeda Pharmaceutical Company)
https://en.wikipedia.org/wiki/Takeda_Pharmaceutical_Company
Title: TBA

iTHES Colloquium in November 2015

Date: Nov.10 (Tues) 15:00-16:30
Place: big conference room (2nd floor of the main cafeteria)
Speaker: Kazuyuki Aihara (Univ. Tokyo)
http://www.sat.t.u-tokyo.ac.jp/aihara/
Title: TBA

## Paper of the week

CFT's Loose Ends Tsukasa Tada (ithes-phys)

In the paper coauthored with Prof. Nobuyuki Ishibashi of Tsukuba University [1], we argued that there is a whole new class of two-dimensional conformal field theories (CFTs). What we found was that if one simply uses $L_0-(L_{1}+L_{-1})/2$ as the Hamiltonian as opposed to $L_0$, one can obtain a new conformal field theory with the same central charge but continuous Virasoro algebra. As implicated by the emergence of continuous Virasoro algebra, the new theory exhibits continuous spectrum and the size of spatial dimension is infinitely large.

The distinctiveness of the above choice of $L_0-(L_{1}+L_{-1})/2$, stems from the $sl(2,\mathbb{R})$ subalgebra of the Virasoro algebra. If one invokies the similarity with Lorentz transformation, $L_0-(L_{1}+L_{-1})/2$ can be interpreted as massless limit or light-front treatment of the original $L_0$.

This procedure is also related with the phenomenon called sine-square deformation (SSD) found in the study of quantum statistical systems. When SSD is applied for CFT, it yields exactly the same Hamiltonian described above. The significance of SSD is, the vacuum sate of sine-square deformed system, which is deformed but apparently open boundary system, is the same vacuum state of the closed boundary system without SSD. This coincidence of the vacuum state between open and closed boundary conditions was somewhat mysterious. Now we can understand this as follows. One spatial dimension where CFT resides, may or may not have end points. However, this is irrelevant since the length of the space is infinite and the end points, if there are, can not be reached.

CFT is very basic tool for the study of both string theory and the low-deimensional quantum systems. Therefore it has been thoroughly investigated, classified, applied. Therefore, it is interesting that there is still such a novel aspect of CFT which had been waiting to be uncovered.

The moral here is, CFT does have loose ends, but you cannot tie them up, because they are infinitely far apart!

[1] N. Ishibashi and T. Tada, 'Infinite circumference limit of conformal field theory,’ J. Phys. A: Math. Theor. 48 (2015) 315402