# Symmetries of the refined D1/D5 BPS spectrum

## Abstract

We examine the large *N* 1/4-BPS spectrum of the symmetric orbifold CFT Sym ^{N} ( *M* ) deformed to the supergravity point in moduli space for *M* = *K*3 and *T* ^{4}. We consider refinement under both left- and right-moving SU(2) _{R} symmetries of the superconformal algebra, and decompose the spectrum into characters of the algebra. We find that at large *N* the character decomposition satisfies an unusual property, in which the degeneracy only depends on a certain linear combination of left- and right-moving quantum numbers, suggesting deeper symmetry structure. Furthermore, we consider the action of discrete symmetry groups on these degeneracies, where certain subgroups of the Conway group are known to play a role. We also comment on the potential for larger discrete symmetry groups to appear in the large *N* limit.

- Authors:

- Stanford Univ., Stanford, CA (United States). Stanford Inst. for Theoretical Physics
- Harvard Univ., Cambridge, MA (United States). Center for the Fundamental Laws of Nature

- Publication Date:

- Research Org.:
- Harvard Univ., Cambridge, MA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1505833

- Grant/Contract Number:
- SC0007870

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 11; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT Correspondence; Conformal and W Symmetry; Conformal Field Theory; Extended Supersymmetry

### Citation Formats

```
Benjamin, Nathan, and Harrison, Sarah M. Symmetries of the refined D1/D5 BPS spectrum. United States: N. p., 2017.
Web. doi:10.1007/jhep11(2017)091.
```

```
Benjamin, Nathan, & Harrison, Sarah M. Symmetries of the refined D1/D5 BPS spectrum. United States. doi:10.1007/jhep11(2017)091.
```

```
Benjamin, Nathan, and Harrison, Sarah M. Wed .
"Symmetries of the refined D1/D5 BPS spectrum". United States. doi:10.1007/jhep11(2017)091. https://www.osti.gov/servlets/purl/1505833.
```

```
@article{osti_1505833,
```

title = {Symmetries of the refined D1/D5 BPS spectrum},

author = {Benjamin, Nathan and Harrison, Sarah M.},

abstractNote = {We examine the large N 1/4-BPS spectrum of the symmetric orbifold CFT SymN (M ) deformed to the supergravity point in moduli space for M = K3 and T 4. We consider refinement under both left- and right-moving SU(2)R symmetries of the superconformal algebra, and decompose the spectrum into characters of the algebra. We find that at large N the character decomposition satisfies an unusual property, in which the degeneracy only depends on a certain linear combination of left- and right-moving quantum numbers, suggesting deeper symmetry structure. Furthermore, we consider the action of discrete symmetry groups on these degeneracies, where certain subgroups of the Conway group are known to play a role. We also comment on the potential for larger discrete symmetry groups to appear in the large N limit.},

doi = {10.1007/jhep11(2017)091},

journal = {Journal of High Energy Physics (Online)},

number = 11,

volume = 2017,

place = {United States},

year = {2017},

month = {11}

}

Works referenced in this record:

##
Six-dimensional supergravity on S3 × AdS3 and 2d conformal field theory

journal, May 1999

- de Boer, Jan
- Nuclear Physics B, Vol. 548, Issue 1-3

##
Counting spinning dyons in maximal supergravity: the Hodge-elliptic genus for tori

journal, August 2017

- Benjamin, Nathan; Kachru, Shamit; Tripathy, Arnav
- Letters in Mathematical Physics, Vol. 107, Issue 11

##
A holographic dual for string theory on AdS3×S3×S3×S1

journal, August 2017

- Eberhardt, Lorenz; Gaberdiel, Matthias R.; Li, Wei
- Journal of High Energy Physics, Vol. 2017, Issue 8

##
Equivariant K3 invariants

journal, January 2017

- Cheng, Miranda C. N.; Duncan, John F. R.; Harrison, Sarah M.
- Communications in Number Theory and Physics, Vol. 11, Issue 1

##
A refined count of BPS states in the D1/D5 system

journal, June 2017

- Benjamin, Nathan
- Journal of High Energy Physics, Vol. 2017, Issue 6

##
BPS spectrum on AdS3×S3×S3×S1

journal, March 2017

- Eberhardt, Lorenz; Gaberdiel, Matthias R.; Gopakumar, Rajesh
- Journal of High Energy Physics, Vol. 2017, Issue 3

##
Umbral Moonshine and K3 Surfaces

journal, June 2015

- Cheng, Miranda C. N.; Harrison, Sarah
- Communications in Mathematical Physics, Vol. 339, Issue 1

##
The D1/D5 system and singular CFT

journal, April 1999

- Seiberg, Nathan; Witten, Edward
- Journal of High Energy Physics, Vol. 1999, Issue 04

##
A Hiker's Guide to K3.¶Aspects of N= (4,4) Superconformal Field Theory¶with Central Charge c= 6

journal, January 2001

- Nahm, Werner; Wendland, Katrin
- Communications in Mathematical Physics, Vol. 216, Issue 1

##
Heisenberg Algebra and Hilbert Schemes of Points on Projective Surfaces

journal, March 1997

- Nakajima, Hiraku
- The Annals of Mathematics, Vol. 145, Issue 2

##
No more walls! A tale of modularity, symmetry, and wall crossing for 1/4 BPS dyons

journal, May 2017

- Paquette, Natalie M.; Volpato, Roberto; Zimet, Max
- Journal of High Energy Physics, Vol. 2017, Issue 5

##
Black rings

journal, September 2006

- Emparan, Roberto; Reall, Harvey S.
- Classical and Quantum Gravity, Vol. 23, Issue 20

##
Search for a holographic dual to $\textit{AdS}_3\times S^3\times S^3\times S^1$

journal, January 2005

- Gukov, Sergei; Martinec, Emil; Moore, Gregory
- Advances in Theoretical and Mathematical Physics, Vol. 9, Issue 3

##
On symmetries of N $$ \mathcal{N} $$ = (4, 4) sigma models on T 4

journal, August 2014

- Volpato, Roberto
- Journal of High Energy Physics, Vol. 2014, Issue 8

##
Character formulas for the N = 4 superconformal algebra

journal, January 1988

- Eguchi, Tohru; Taormina, Anne
- Physics Letters B, Vol. 200, Issue 3

##
The Hodge-Elliptic Genus, Spinning BPS States, and Black Holes

journal, May 2017

- Kachru, Shamit; Tripathy, Arnav
- Communications in Mathematical Physics, Vol. 355, Issue 1

##
A note on toroidal compactification of heterotic string theory

journal, January 1987

- Narain, K. S.; Sarmadi, M. H.; Witten, E.
- Nuclear Physics B, Vol. 279, Issue 3-4

##
Microscopic origin of the Bekenstein-Hawking entropy

journal, June 1996

- Strominger, Andrew; Vafa, Cumrun
- Physics Letters B, Vol. 379, Issue 1-4

##
Unitary representations of the N=4 superconformal algebra

journal, September 1987

- Eguchi, Tohru; Taormina, Anne
- Physics Letters B, Vol. 196, Issue 1

##
Characters of the N = 4 superconformal algebra with two central extensions (II). Massless representations

journal, April 1990

- Petersen, J. L.; Taormina, A.
- Nuclear Physics B, Vol. 333, Issue 3

##
Quarter-BPS states in orbifold sigma models with ADE singularities

journal, June 2017

- Wong, Kenny
- Journal of High Energy Physics, Vol. 2017, Issue 6

##
Notes on the K3 Surface and the Mathieu Group *M* _{24}

journal, March 2011

- Eguchi, Tohru; Ooguri, Hirosi; Tachikawa, Yuji
- Experimental Mathematics, Vol. 20, Issue 1

##
Superconformal algebras in two dimensions with N=4

journal, July 1988

- Sevrin, A.; Troost, W.; Van Proeyen, A.
- Physics Letters B, Vol. 208, Issue 3-4

##
*AdS* _{3} black holes and a stringy exclusion principle

journal, December 1998

- Maldacena, Juan; Strominger, Andrew
- Journal of High Energy Physics, Vol. 1998, Issue 12

##
Black hole entropy in M-Theory

journal, December 1997

- Maldacena, Juan; Strominger, Andrew; Witten, Edward
- Journal of High Energy Physics, Vol. 1997, Issue 12

##
Elliptic Genera of Symmetric Products and Second Quantized Strings

journal, April 1997

- Dijkgraaf, Robbert; Moore, Gregory; Verlinde, Erik
- Communications in Mathematical Physics, Vol. 185, Issue 1

##
Instanton strings and hyper-Kähler geometry

journal, March 1999

- Dijkgraaf, Robbert
- Nuclear Physics B, Vol. 543, Issue 3

##
Characters of the N = 4 superconformal algebra with two central extensions

journal, February 1990

- Petersen, J. L.; Taormina, A.
- Nuclear Physics B, Vol. 331, Issue 3

##
Symmetries of K3 sigma models

journal, January 2012

- Gaberdiel, Matthias R.; Hohenegger, Stefan; Volpato, Roberto
- Communications in Number Theory and Physics, Vol. 6, Issue 1

##
Perverse sheaves and the cohomology of Hilbert schemes of smooth algebraic surfaces

journal, December 1993

- G�ttsche, Lothar; Soergel, Wolfgang
- Mathematische Annalen, Vol. 296, Issue 1

##
K3 surfaces, $\mathcal{N}=4$ dyons and the Mathieu group $M_{24}$

journal, January 2010

- Cheng, Miranda C. N.
- Communications in Number Theory and Physics, Vol. 4, Issue 4