(Mock) Modularity, Moonshine and String Theory

Conference Date: 
Monday, April 13, 2015 (All day) to Friday, April 17, 2015 (All day)
Scientific Areas: 
String Theory

 

Modular and mock modular forms have appeared in new and intriguing roles in relation to Mathieu and Umbral moonshine.  They also appear in studies of the quantum geometry of Calabi-Yau manifolds, three dimensional gravity, and other aspects of string theory.  This workshop will be focused on the recent developments in these intertwined directions.

This workshop is also part of the UNIFY network.  Participants from the UNIFY nodes are welcome to register and participate.

Registration for this workshop is now closed.

Sponsorship for this workshop has been provided by:

  • Miranda Cheng, University of Amsterdam
  • John Duncan, Case Western Reserve University
  • Matthias Gaberdiel, ETH Zurich
  • Terry Gannon, University of Alberta
  • Sarah Harrison, Harvard University
  • Jeffrey Harvey, University of Chicago
  • Shamit Kachru, Stanford University
  • Christoph Keller, Rutgers University
  • Heeyeon Kim, Perimeter Institute
  • Albrecht Klemm, University of Bonn
  • Ching Hung Lam, Institute of Mathematics, Academia Sinica
  • Geoffrey Mason, Universityof California, Santa Cruz
  • Greg Moore, Rutgers University
  • Sameer Murthy, Kings College, London
  • Hirosi Ooguri, California Institute of Technology
  • Daniel Persson, Chalmers University of Technology
  • Anne Taormina, Durham University
  • Roberto Volpato, SLAC & Stanford University
  • Katrin Wendland, University of Freiburg
  • Nathan Benjamin, Stanford University
  • Lakshya Bhardwaj, Perimeter Institute
  • Christopher Brust, Perimeter Institute
  • Miranda Cheng, University of Amsterdam
  • Nima Doroud, University of Cambridge
  • John Duncan, Case Western Reserve University
  • Matthias Gaberdiel, ETH Zurich
  • Terry Gannon, University of Alberta
  • Jaume Gomis, Perimeter Institute
  • Sarah Harrison, Harvard University
  • Jeffrey Harvey, University of Chicago
  • Shamit Kachru, Stanford University
  • Christoph Keller, Rutgers University
  • Heeyeon Kim, Perimeter Institute
  • Albrecht Klemm, University of Bonn
  • Peter Korotev, Perimeter Institute
  • Ching Hung Lam, Institute of Mathematics, Academia Sinica
  • Geoffrey Mason, Universityof California, Santa Cruz
  • Greg Moore, Rutgers University
  • Seyed Faroogh Moosavian, Perimeter Institute
  • Sameer Murthy, Kings College, London
  • Hirosi Ooguri, California Institute of Technology
  • Natalie Paquette, Stanford University
  • Daniel Persson, Chalmers University of Technology
  • Callum Quigley, University of Alberta
  • Miroslav Rapcak, Perimeter Institute
  • Anne Taormina, Durham University
  • Roberto Volpato, SLAC & Stanford University
  • Katrin Wendland, University of Freiburg
  • Daniel Whalen, Stanford University
  • Jie Zhou, Perimeter Institute

Monday, April 13, 2015

Time

Event

Location

9:30 – 10:00am

Registration

Reception

10:00 – 10:05am

Welcome and Opening Remarks

Bob Room

10:05 – 11:00am

Jeffrey Harvey, University of Chicago
Traces of Singular Moduli and Moonshine for the Thompson group

Bob Room

11:00 – 12:00pm

Albrecht Klemm, University of Bonn
TBA

Bob Room

12:00 – 2:00pm

Lunch

Bistro – 2nd Floor

2:00 – 3:00pm

Geoffrey Mason, University of California, Santa Cruz
Symplectic automorphisms of some hyperk\"ahler manifolds

Bob Room

3:00 – 4:00pm

Shamit Kachru, Stanford University
Moonshine at c=12

Bob Room

 

Tuesday, April 14, 2015

Time

Event

Location

10:00 – 11:00am

John Duncan, Case Western Reserve University
Umbral Moonshine Modules

Bob Room

11:00 – 12:00pm

Daniel Persson, Chalmers University of Technology
U-duality, exotic instantons and automorphic forms on Kac-Moody groups

Bob Room

12:00 – 2:00pm

Lunch Break

Bistro – 2nd Floor

2:00 – 3:00pm

Roberto Volpato, SLAC & Stanford University
Fricke S-duality in CHL models

Bob Room

3:00 – 4:00pm

Miranda Cheng, University of Amsterdam
Optimal Jacobi Forms and Mock Theta Functions

Bob Room

6:00pm Onwards

Reception

Bistro – 2nd Floor

 

Wednesday, April 15, 2015

Time

Event

Location

10:00 – 11:00am

Katrin Wendland, University of Freiburg
How does extended supersymmetry affect the elliptic genus?

Bob Room

11:00 – 12:00pm

Christoph Keller, Rutgers University
Modular invariance and holographic CFTs

Bob Room

12:00 – 12:15

Conference Photo

TBA

12:15 – 2:00pm

Lunch Break

Bistro – 2nd Floor

2:00 - 3:30 pm Paul Ginsparg, Cornell University
Colloquium:  At a Physics/Infosci Intersection
 

3:30 – 4:30pm

Ching Hung Lam, Institute of Mathematics, Academia Sinica
On holomorphic vertex operator algebras of central charge 24

Bob Room

 

Thursday, April 16, 2015

Time

Event

Location

10:00 – 11:00am

Hirosi Ooguri, California Institute of Technology
Analytic Bootstrap Bounds

Bob Room

11:00 – 12:00pm

Terry Gannon, University of Alberta
Thoughts stolen from the enemy

Bob Room

12:00 – 2:00pm

Lunch Break

Bistro – 2nd Floor

2:00 – 3:00pm

Anne Taormina, Durham University
Signatures of Mathieu Moonshine in Z_2-orbifolds of Conformal Field Theories

Bob Room

3:00 – 4:00pm

Heeyeon Kim, Perimeter Institute
Quiver Quantum Mechanics and Wall-Crossing 

Bob Room

 

Friday, April 17, 2015

Time

Event

Location

10:00 – 11:00am

Greg Moore, Rutgers University
Measuring the Elliptic Genus

Bob Room

11:00 – 12:00pm

Sarah Harrison, Harvard University
Umbral Moonshine and K3 Surfaces

Bob Room

12:00 – 2:00pm

Lunch Break

Bistro – 2nd Floor

2:00 – 3:00pm

Sameer Murthy, King's College London
ADE Little string theories, Mock modular forms, and Umbral moonshine

Bob Room

3:00 – 4:00pm

Matthias Gaberdiel, ETH Zurich
Higher Spins & Strings

Bob Room

 

Miranda Cheng, University of Amsterdam

Optimal Jacobi Forms and Mock Theta Functions

John Duncan, Case Western Reserve University

Umbral Moonshine Modules

Umbral moonshine attaches mock modular forms and meromorphic Jacobi forms to automorphisms of the Niemeier lattices. It is now known that this association can be recovered from specific, graded modules for the Niemeier lattice automorphism groups. We will describe recent progress in a program to realize these modules explicitly. 

Matthias Gaberdiel, ETH Zurich

Higher Spins & Strings

Terry Gannon, University of Alberta

Thoughts stolen from the enemy

Subfactors and VOAs should both describe CFT, but what is relatively easy in one formulation can be very difficult in the other. In my talk I'll describe lessons the VOA world can learn from the subfactor one.

Sarah Harrison, Harvard University

Umbral Moonshine and K3 Surfaces

Recently, 23 cases of umbral moonshine, relating mock modular forms and finite groups, have been discovered in the context of the 23 even unimodular Niemeier lattices. One of the 23 cases in fact coincides with the so-called Mathieu moonshine, discovered in the context of K3 non-linear sigma models. Here we establish a uniform relation between all 23 cases of umbral moonshine and K3 sigma models, and thereby take a first step in placing umbral moonshine into a geometric and physical context. This is achieved by relating the ADE root systems of the Niemeier lattices to the ADE du Val singularities that a K3 surface can develop, and the configuration of smooth rational curves in their resolutions. A geometric interpretation of our results is given in terms of the marking of K3 surfaces by Niemeier lattices.

Jeffrey Harvey, University of Chicago

Traces of Singular Moduli and Moonshine for the Thompson group

We observe a relationship between the representation theory of the Thompson sporadic group and a weakly holomorphic modular form of weight one-half that appears in Zagier's work on traces of singular moduli and Borcherds products. We conjecture the existence of an infinite dimensional graded module for the Thompson group and use the observed relationship to propose a  McKay-Thompson series for each conjugacy class of the Thompson group and then  construct weakly holomorphic weight one-half forms at higher level  that coincide with the proposed McKay-Thompson series.  We also observe a discriminant property in this conjectured moonshine for the Thompson group that is closely related to the discriminant property conjectured to exist in Umbral Moonshine.

Shamit Kachru, Stanford University

Moonshine at c=12

Christoph Keller, Rutgers University

Modular invariance and holographic CFTs

Modular invariance plays an important role in AdS3/CFT2 holography. I discuss the structure of non-holomorphic CFT partition functions, namely in what sense the light spectrum determines the heavy spectrum and how to construct example partition functions using Poincare series. This yields necessary conditions on the spectrum of holographic CFTs. Finally I will discuss permutation orbifolds as examples of such theories.

Heeyeon Kim, Perimeter Institute

Quiver Quantum Mechanics and Wall-Crossing 

I will talk about computation of the Witten index of 1d N=4 gauged linear sigma model which describes wall-crossing of BPS states in 4d N=2 theories. In the phase where the gauge group is broken to a finite group, the index is expressed as the JK-residue integral. Using this result, I am going to examine large-rank behaviour of the Kronecker quivers which describes the most simplest wall-crossing phenomena. I will also talk about how the refined Witten indices of quivers are preserved under the mutation process.

Ching Hung Lam, Institute of Mathematics, Academia Sinica

On holomorphic vertex operator algebras of central charge 24

I will talk about the recent progress on the classification of (strongly regular) holomorphic vertex operator algebras of central charge 24. In particular, I will discuss a  construction of certain holomorphic vertex operator algebras of central charge 24 using orbifold construction associated to inner automorphisms.  This talk is based on a joint work with Hiroki Shimakura.

Geoffrey Mason, University of California, Santa Cruz

Symplectic automorphisms of some hyperk\"ahler manifolds

Greg Moore, Rutgers University

Measuring the Elliptic Genus

This talk is based on the recent paper co-authored with N. Benjamin, M. Cheng, S. Kachru, and N. Paquette.

Sameer Murthy, King's College London

ADE Little string theories, Mock modular forms, and Umbral moonshine

Hirosi OoguriCalifornia Institute of Technology

Analytic Bootstrap Bounds

Daniel Persson, Chalmers University of Technology

U-duality, exotic instantons and automorphic forms on Kac-Moody groups

Anne Taormina, Durham University

Signatures of Mathieu Moonshine in Z_2-orbifolds of Conformal Field Theories

Roberto Volpato, SLAC & Stanford University

Fricke S-duality in CHL models

We consider dual pairs of four dimensional heterotic/type IIA CHL models with 16 space-time supersymmetries.  We provide strong evidence for the existence of an S-duality acting on the heterotic axion-dilaton by a Fricke involution S --> -1/NS, where N is the order of the orbifold symmetry. While most models are self-dual, in some cases S-duality relates the CHL model to a compactification of type IIA on an orbifold of T^6. We provide a simple criterion to determine whether a model is self-dual or not. Finally, we argue that in self-dual CHL models the lattices of electric and magnetic charges must be N-modular and verify this prediction.

Katrin Wendland, University of Freiburg

How does extended supersymmetry affect the elliptic genus?

The elliptic genus of K3 and its decomposition into characters of the N=4 superconformal algebra of associated conformal field theories can be viewed as the outset of Mathieu Moonshine. Thus, extended supersymmetry induces additional properties of the elliptic genus, which so far lack a satisfactory geometric interpretation. We investigate the implications of this decomposition on geometric structures that underlie the elliptic genus.
 

Scientific Organizers:

  • Miranda Cheng, University of Amsterdam
  • Matthias Gaberdiel, ETH Zurich
  • Jaume Gomis, Perimeter Institute
  • Shamit Kachru, Stanford University