String-Math 2016 : June 27-July 2, 2016, Collège de France, Paris, France / Amir-Kian Kashani-Poor, Ruben Minasian, Nikita Nekrasov, Boris Pioline, editors.

Format:

Book

Conference/Event

Contributor:

Kashani-Poor, Amir-Kian, 1974- editor.

Minasian, Ruben, 1967- editor.

Nekrasov, Nikita, 1973- editor.

Pioline, Boris, 1972- editor.

Conference Name:

String-Math (Conference) (2016 : Paris, France)

Series:

Proceedings of symposia in pure mathematics ; Volume 98.

Proceedings of symposia in pure mathematics ; Volume 98

Language:

English

Subjects (All):

Geometry, Algebraic--Congresses.

Geometry, Algebraic.

Quantum theory--Mathematics--Congresses.

Quantum theory.

Physical Description:

1 online resource (314 pages).

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2018]

Summary:

This volume contains the proceedings of the conference String-Math 2016, which was held from June 27-July 2, 2016, at Collége de France, Paris, France. String-Math is an annual conference covering the most significant progress at the interface of string theory and mathematics. The two fields have had a very fruitful dialogue over the last thirty years, with string theory contributing key ideas which have opened entirely new areas of mathematics and modern mathematics providing powerful concepts and tools to deal with the intricacies of string and quantum field theory. The papers in this volume cover topics ranging from supersymmetric quantum field theories, topological strings, and conformal nets to moduli spaces of curves, representations, instantons, and harmonic maps, with applications to spectral theory and to the geometric Langlands program.

Contents:

Cover

Title page

Contents

Preface

Three-dimensional \cN=4 gauge theories in omega background

1. Introduction

2. Setup

3. Hilbert space

4. Monopole operators

5. Boundary conditions and overlaps

6. Vortex quantum mechanics

Acknowledgements

References

3d supersymmetric gauge theories and Hilbert series

2. Moduli space of supersymmetric vacua and chiral ring

3. The Hilbert series

4. 3 \cN=2 gauge theories vs 4 \cN=1 gauge theories

5. 't Hooft monopole operators

6. Monopole formula for the Hilbert series of 3 \cN≥2 gauge theories

7. Coulomb branch of 3 \cN=4 gauge theories

8. Moduli spaces of 3 \cN=2 theories and Hilbert series

9. Conclusion

Quantized Coulomb branches of Jordan quiver gauge theories and cyclotomic rational Cherednik algebras

1(i).

1(ii).

Acknowledgments

2. The case with no framing

3. Poisson brackets

4. Cherednik algebras

4(i). Definitions

4(ii). Dunkl operators

4(iii). Rational Demazure-Lusztig operators

5. Cyclotomic rational Cherednik algebras

6. Affine Yangian of \gl(1)

6(i). Presentation

6(ii). From Yangian to difference operators

6(iii). Proof

6(iv). Automorphism

6(v). Shifted Yangian

Appendix A.

Appendix B.

Supersymmetric field theories and geometric Langlands: The other side of the coin

2. Review

3. Defects of co-dimension two and surface operators

4. Partition functions versus conformal blocks

5. Another type of surface operators

6. Recovering the geometric Langlands correspondence

7. Sigma model interpretation?

Appendix A. Hitchin's moduli spaces

A journey from the Hitchin section to the oper moduli

2. Enumeration of ribbon graphs.

3. A walk into the woods of Higgs bundles and connections

4. From Higgs bundles to quantum curves

5. The metamorphosis of quantum curves into opers

6. Hitchin moduli spaces for the Lie group = ᵣ(ℂ)

7. The limit oper of Gaiotto's correspondence and the quantum curve

8. Conclusion

S-duality of boundary conditions and the Geometric Langlands program

1. Introduction and conclusions

2. Neumann-like boundary conditions and matter interfaces

3. A rich example: Particle-vortex duality in (1) gauge theory

4. Bifundamental and fundamental interfaces

5. General NS5 and D5 interfaces for unitary groups

6. Ortho-symplectic examples

7. Tri-fundamental (2)× (2)× (2) interface

8. More examples with gauge group reductions

9. D-modules

10. Sheafs on the moduli space of local systems

Appendix A. Lagrangian submanifolds and generating functions

Appendix B. Supersymmetric Berry connections for \CN=4 SQM

Appendix C. The category of BBB branes

Appendix D. Gauge group reductions

Pure (2) gauge theory partition function and generalized Bessel kernel

2. Isomonodromy and Riemann-Hilbert setup

3. Fredholm determinant representation

4. Series over Young diagrams

Reduction for (3) pre-buildings

2. Spectral networks in

3. The initial construction

4. Structures

5. The refraction property

6. Reduction

7. The new construction

8. Scholium

9. Further questions

Conformal nets are factorization algebras

2. Factorization algebras

3. Proofs

4. An application

5. Appendix

Acknowledgement

Contracting the Weierstrass locus to a point

Introduction

1. Rational maps \forg₂ and.

2. Curves of genus 2

Spectral theory and mirror symmetry

2. A problem in spectral theory

3. From topological strings to spectral theory

4. From spectral theory to topological strings

5. Outlook

Back Cover.

Notes:

Includes bibliographical references.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

1-4704-4770-3

OCLC:

1043655297