REVIEW
A brief review of "little string theories"
High Energy Physics - Theory · Submitted 18 Nov 1999 · 30 references
Pith's verdict: A clean, honest snapshot of the little-string-theory program as of 1999; the one soft spot is the limiting-temperature claim in §4, and the paper mostly flags it itself.
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Referee report
The paper
The paper claims
Taking the string coupling to zero on a stack of coincident NS5-branes leaves a non-gravitational six-dimensional theory whose dynamics is still governed by the string scale.
The reading
What carries the argument
Three constructions carry the argument. The first is the decoupling limit itself: the NS5-brane couplings are held fixed as $g_s to 0$ because the brane tension scales as $1/g_s^2$ while the gravitational coupling scales as $g_s^2$, so the branes' mutual interactions survive while the bulk decouples. The second is the discrete light-cone definition: the $A_{k-1}$ $(2,0)$ theory with $N$ units of light-cone momentum is the $1+1$ dimensional $N=(4,4)$ $\sigma$ model on the $4Nk$-dimensional moduli space of $N$ instantons in $SU(k)$ on $mathbb{R}^4$, equivalently the low-energy limit of the Higgs branch of $U(N)$ SQCD with one adjoint and $k$ fundamental hypermultiplets, compactified on a circle of radius $Sigma = 1/(R M_s^2)$; the $(1,1)$ version is a quiver gauge theory with bifundamental matter and a Wilson line. The third is the holographic dual: M theory on a background with metric $l_p^{-2} ds^2 = H^{-1/3} dx_6^2 + H^{2/3}(dx_{11}^2 + dU^2 + U^2 dOmega_3^2)$ and $H = sum_j pi k / (U^2 + (x_{11} - 2pi j M_s^2)^2)^{3/2}$, which reduces at small $U$ to $AdS_7 times S^4$ and at large $U$ to a type IIA linear dilaton background $ds^2 = dx_6^2 + dvarphi^2 + k l_s^2 dOmega_3^2$ with $g_s(varphi) = e^{-varphi/(sqrt{k} l_s)}$.
Extended reading notes
Core claim
The central claim is that the $g_s to 0$ limit of $k$ overlapping NS5-branes in type IIA or type IIB string theory is a non-trivial, non-gravitational, Lorentz-invariant six-dimensional theory with 16 supercharges, parametrized only by the string scale $M_s$ and the integer $k$. The type IIA case gives $N=(2,0)$ supersymmetry and the type IIB case $N=(1,1)$; the low-energy limit of the first is the $(2,0)$ superconformal theory on $k$ M5-branes, and of the second a $U(k)$ gauge theory with $g_{YM}^2 = 1/M_s^2$. A web of dualities supplies equivalent definitions: the $(2,0)$ theory also arises from $k$ M5-branes on a vanishing transverse circle with $R M_p^3 = M_s^2$ fixed, the $(1,1)$ theory from $k$ D5-branes at $g_s to infty$, and both from type II string theory on an $A_{k-1}$ singularity at $g_s to 0$. The review's own framing is that these theories sit between local field theory and full string theory, and that their interest lies precisely in properties such as T-duality and a Hagedorn spectrum that were previously thought to require gravity.
Load-bearing premise
The light-cone construction is presented as an explicit non-perturbative definition of these theories, but it rests on the unproved premise that the finite-$N$ two-dimensional theory, extrapolated to large $N$, actually reproduces the six-dimensional theory; the review says only that this is believed and concedes that no dynamical computation has yet been done with it.
Editorial extensions
If this is right
- T-duality survives in a non-gravitational setting: the $(2,0)$ $A_{k-1}$ theory on a circle of radius $R$ is dual to the $(1,1)$ theory on a circle of radius $1/(M_s^2 R)$, so after toroidal compactification the theory has no unique energy-momentum tensor.
- Every such theory contains BPS-saturated strings of tension $T = M_s^2$ at the origin of moduli space, giving string-like excitations with no gravity attached.
- The high-energy density of states is exponential in the energy density, with a limiting temperature $T_H simeq M_s/sqrt{6k}$ above which the canonical ensemble cannot be defined.
- Position-space correlation functions appear not to exist below separations of order $1/T_H$, so the theories have no local operators at shorter distances.
- The moduli space is exactly $mathbb{R}^{4k}/S_k$ for the $(1,1)$ theory and $(mathbb{R}^4 times S^1)^k/S_k$ for the $(2,0)$ theory, receiving no quantum corrections, which gives a controlled window on the low-energy dynamics.
Reading between the lines
- If the light-cone definitions are correct, these are the first known non-gravitational theories with a Hagedorn density of states, which suggests that Hagedorn behaviour in ordinary string theory is a property of string-scale dynamics rather than of gravity.
- Placing holography in a linear dilaton background, where the string coupling vanishes at the boundary, means bulk supergravity is weakly coupled exactly where boundary data are prescribed; this may make such backgrounds a cleaner testing ground for holographic renormalization than $AdS$ spaces.
- The review's open question about whether the theory becomes weakly coupled at high energy has a natural reading: since $g_s(varphi) to 0$ toward the boundary, high-energy probes may see a nearly free theory, an asymptotic freedom of a kind not yet made precise.
- The claim that correlators fail below $1/T_H$ suggests a minimum length set by the Hagedorn temperature rather than by $M_s$; a computation that separates these two scales would be a sharp test of how non-local the theory really is.
Original abstract
This is a brief review of the current state of knowledge on "little string theories", which are non-gravitational theories having several string-like properties. We focus on the six dimensional maximally supersymmetric "little string theories" and describe their definition, some of their simple properties, the motivations for studying them, the DLCQ and holographic constructions of these theories and their behaviour at finite energy density. (Contribution to the proceedings of Strings '99 in Potsdam, Germany.)
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
This is a brief review of the current state of knowledge on "little string theories", which are non-gravitational theories having several string-like properties. We focus on the six dimensional maximally supersymmetric "little string theories" and describe their definition, some of their simple properties, the motivations for studying them, the DLCQ and holographic constructions of these theories and their behaviour at finite energy density. (Contribution to the proceedings of Strings '99 in Potsdam, Germany.)
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | This is a brief review of the current state of knowledge on "little string theories", which are non-gravitational theories having several string-like properties. | contribution 0.61 | 0.14 | 0.14 | asserted 0.97 |
| s1 | We focus on the six dimensional maximally supersymmetric "little string theories" and describe their definition, some of their simple properties, the motivations for studying them, the DLCQ and holographic constructions of these theories and their behaviour at finite energy density. | contribution 1.00 | 0.42 | 0.10 | asserted 0.87 |
| s2 | (Contribution to the proceedings of Strings '99 in Potsdam, Germany.) | background 0.84 | 0.04 | 0.02 | unclear 0.91 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
References
How the literature uses it
76 arXiv papers cite this in 84 sentences
Papers citing it · 21 sentences without a confident label
Cites it as background 61 papers
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A different theory where the bulk graviton propagator is a gapped continuum appeared in a different class of 5D backgrounds, the so-called linear dilaton (LD) [ref] metric, which is known to be dual to Little String Theories [ref] .
Massive Graviton Dark Matter from a Gapped Continuum · Introduction · 0.87
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The dynamics of coincident fivebranes in string theory is governed by little string theory, a somewhat mysterious non-gravitational, nonlocal theory in six spacetime dimensions [ref] (for reviews, see [ref] ).
Little Strings, Long Strings, and Fuzzballs · Fivebrane dynamics · 1.00
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Interestingly enough there is another warped geometry for which the holographic dual is known: the linear dilaton (LD) background metric for which the holographic dual is Little String Theory (LST), a six-dimensional theory compactified on a torus [ref] .
Linear Dilaton in Cosmology and Particle Physics · Introduction · 0.85
Discussion
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