nLab little string theory

Idea

A limit of the worldvolume theory of the NS5-brane, which is a string theory of “little strings” in six dimensions.

Related concepts

• D=6 N=(2,0) SCFT

Table of branes appearing in supergravity/string theory (for classification see at brane scan).

brane	in supergravity	charged under gauge field	has worldvolume theory
black brane	supergravity	higher gauge field	SCFT
D-brane	type II	RR-field	super Yang-Mills theory
$(D = 2n)$	type IIA	$\,$	$\,$
D(-2)-brane	$\,$	$\,$
D0-brane	$\,$	$\,$	BFSS matrix model
D2-brane	$\,$	$\,$	$\,$
D4-brane	$\,$	$\,$	D=5 super Yang-Mills theory with Khovanov homology observables
D6-brane	$\,$	$\,$	D=7 super Yang-Mills theory
D8-brane	$\,$	$\,$
$(D = 2n+1)$	type IIB	$\,$	$\,$
D(-1)-brane	$\,$	$\,$	$\,$
D1-brane	$\,$	$\,$	2d CFT with BH entropy
D3-brane	$\,$	$\,$	N=4 D=4 super Yang-Mills theory
D5-brane	$\,$	$\,$	$\,$
D7-brane	$\,$	$\,$	$\,$
D9-brane	$\,$	$\,$	$\,$
(p,q)-string	$\,$	$\,$	$\,$
(D25-brane)	(bosonic string theory)
NS-brane	type I, II, heterotic	circle n-connection	$\,$
string	$\,$	B2-field	2d SCFT
NS5-brane	$\,$	B6-field	little string theory
D-brane for topological string			$\,$
A-brane			$\,$
B-brane			$\,$
M-brane	11D SuGra/M-theory	circle n-connection	$\,$
M2-brane	$\,$	C3-field	ABJM theory, BLG model
M5-brane	$\,$	C6-field	6d (2,0)-superconformal QFT
M9-brane/O9-plane			heterotic string theory
M-wave
topological M2-brane	topological M-theory	C3-field on G₂-manifold
topological M5-brane	$\,$	C6-field on G₂-manifold
S-brane
SM2-brane, membrane instanton
M5-brane instanton
D3-brane instanton
solitons on M5-brane	6d (2,0)-superconformal QFT
self-dual string		self-dual B-field
3-brane in 6d

References

General

The original reference is

• Nathan Seiberg, New theories in six dimensions and matrix description of M-theory on $T^5$ and $T^5/\mathbb{Z}_2$ Phys. Lett. B408 (1997) 98–104 (arXiv:hep-th/9705221)

Review is in

• Ofer Aharony, A brief review of “little string theories” , Class. Quant. Grav. 17 (2000) 929–938,

  (arXiv:hep-th/9911147).

• David Kutasov, Introduction to Little String Theory, Lectures 2001 (pdf)

Little string theories on heterotic string theory NS5-branes with $N = (1,0)$ supersymmetry:

• E. Gava, K.S. Narain, M.H. Sarmadi, Little String Theories in Heterotic Backgrounds, Nucl.Phys. B626 (2002) 3-25 (arXiv:hep-th/0112200)

and via F-theory methods:

• Michele Del Zotto, Muyang Liu, Paul-Konstantin Oehlmann, 6D Heterotic Little String Theories and F-theory Geometry: An Introduction [arXiv:2303.13502]

The T-duality between type IIA and type IIB little strings is discussed in

• Jungmin Kim, Seok Kim, Kimyeong Lee, Little strings and T-duality, JHEP 2016:170 (arXiv:1503.07277)

Construction within F-theory is discussed in

• Lakshya Bhardwaj, Michele Del Zotto, Jonathan Heckman, David Morrison, Tom Rudelius, Cumrun Vafa, F-theory and the Classification of Little Strings (arXiv:1511.05565)

See also

• Mina Aganagic, Some mathematical applications of little string theory, talk at Strings 2016 (pdf)

• Joonho Kim, Kimyeong Lee, Little strings on $D_n$ orbifolds (arXiv:1702.03116)

On D=3 N=4 super Yang-Mills theories with compact hyperkähler manifold Coulomb branches obtained by KK-compactification of little string theories:

• Kenneth Intriligator, Compactified Little String Theories and Compact Moduli Spaces of Vacua, Phys. Rev. D61:106005, 2000 (arXiv:hep-th/9909219)

Relation of little string theory to the quantum geometric Langlands correspondence is discussed in

• Mina Aganagic, Edward Frenkel, Andrei Okounkov, Quantum $q$-Langlands Correspondence (arXiv:1701.03146)

also

• Babak Haghighat, Rui Sun, M5 branes and Theta Functions (arXiv:1811.04938)

Discussion with emphasis on terminology from higher gauge theory:

• Michele Del Zotto, Kantaro Ohmori, 2-Group Symmetries of 6D Little String Theories and T-Duality, Ann. Henri Poincaré 22, 2451–2474 (2021) (arXiv:2009.03489,

  doi:10.1007/s00023-021-01018-3)

Open D$p$-brane theories

For light D-branes ending on NS5-branes (see there)

• Rajesh Gopakumar, Shiraz Minwalla, Nathan Seiberg, Andrew Strominger, OM Theory in Diverse Dimensions, JHEP 0008:008, 2000 (arXiv:hep-th/0006062)

• Troels Harmark, Open Branes in Space-Time Non-Commutative Little String Theory, Nucl.Phys. B593 (2001) 76-98 (arXiv:hep-th/0007147)

• Jian Xin Lu, $(1 + p)$-Dimensional Open $D(p - 2)$ Brane Theories, JHEP 0108:049 (2001) [arXiv:hep-th/0102056, doi:10.1088/1126-6708/2001/08/049]

See also

• Dan Israel, Ari Pakman, Jan Troost, D-branes in Little String Theory, Nucl.Phys. B722 (2005) 3-64 (arXiv:hep-th/0502073)

Via the plane wave matrix model

On a double-scaling limit of the BMN matrix model in which aspects of little string theory become visible:

• Hai Lin, Juan Maldacena, Fivebranes from gauge theory, Phys. Rev. D 74 084014 (2006) [arXiv:hep-th/0509235, doi:10.1103/PhysRevD.74.084014]

• Henry Ling, Ali Reza Mohazab, Hsien-Hang Shieh, Greg van Anders, Mark Van Raamsdonk, Little String Theory from a Double-Scaled Matrix Model, JHEP 0610:018 (2006) [arXiv:hep-th/0606014, doi:10.1088/1126-6708/2006/10/018]

• Yuhma Asano, Goro Ishiki, Takaki Matsumoto, Shinji Shimasaki, Hiromasa Watanabe, On the existence of the NS5-brane limit of the plane wave matrix model, PTEP 2023 (2023) 4, 043B01 [arXiv:2211.13716, doi:10.1093/ptep/ptad042]