/
Wolfgang Riedler Self-Dual Vertex Operator Wolfgang Riedler Self-Dual Vertex Operator

Wolfgang Riedler Self-Dual Vertex Operator - PowerPoint Presentation

widengillette
widengillette . @widengillette
Follow
342 views
Uploaded On 2020-07-01

Wolfgang Riedler Self-Dual Vertex Operator - PPT Presentation

Superalgebras and Superconformal Field Theory i n collaboration with Thomas Creutzig amp John Duncan Alberta Number Theory Days Banff 1719032017 Main Question Can a selfdual ID: 791032

theory cft dual type cft theory type dual vertex operator super field conformal eigenvalues moonshine modular bulk voa algebra

Share:

Link:

Embed:

Download Presentation from below link

Download The PPT/PDF document "Wolfgang Riedler Self-Dual Vertex Operat..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.


Presentation Transcript

Slide1

Wolfgang Riedler

Self-Dual Vertex Operator Superalgebras and Superconformal Field Theory

in collaboration with Thomas Creutzig & John Duncan

Alberta Number Theory Days

Banff, 17.-19.03.2017

Slide2

Main Question

Can a self-dual vertex operator algebra (VOA) be identified with a bulk conformal field theory (CFT) in some sense?

Slide3

Moonshine

Slide4

Moonshine

Slide5

Motivation

N=4 superconformal algebra with central charge 6 appears in all of these.

Slide6

Vertex

Operator Super-Algebras

Slide7

Vertex

Operator Super-Algebras

Two remarks

:

In what follows we only consider “nice” VOSAs.

Def.

A

VOSA is

self-dual

if it is rational and has a unique irreducible module.

Slide8

Representations:

Conformal Field Theory

Definition.

as given above is a potential bulk conformal field theory if is modular invariant.

Slide9

Main Question

Can a self-dual vertex operator algebra (VOA) be identified with a bulk conformal field

theory (CFT) in some sense?Yes.

Proposition.

With

W

as above, if

the

S

-matrix of is real and the eigenvalues of the action of

on

W

belong to then is modular invariant.

Slide10

…but we can do better.

Slide11

…but we can do better.

Proposition.

With W as above, if the S-matrix of is real, the eigenvalues of on lie in and the eigenvalues of

on lie in then

the vector

valued function

is

modular.

Slide12

Example: SCFT

of Type D

A connection between sigma models and Conway moonshine.

Slide13

-

Fin -[EOT] – Eguchi,

Ooguri, Tachikawa. “Notes on the K3 Surface and the Mathieu Group M24”, Experiment. Math. Volume 20, Issue 1 (2011), 91-96.[MSV] – Malikov, Schechtman, Vaintrop. “Chiral de

Rham complex”, Comm. Math. Phys. 204 (1999), 439-473.[JD] – Duncan, Mack-Crane. “

Derived Equivalences of K3 Surfaces and Twined Elliptic Genera”

, Res. Math. Sci. (2016) 3:1.

Slide14

A Classification Result

Theorem.

If is a self-dual -cofinite VOSA of CFT type with central charge c 12 then it is isomorphic to one of the following:

Slide15

Example 1.5: Super CFT of Type D

Slide16

Example 2: Super CFT of Type A

Slide17

Example 3: Super CFT of

Gepner Type

Slide18

Modularity

Theorem. [Zhu]

On the upper half plane the characters of a rational, C2-cofinite VOA converge to holomorphic functions. Moreover, the linear space spanned by the limits of characters is invariant under the action of SL2(Z).