Quantum Mechanical Sectors in Thermal N=4 Super Yang-Mills on RxS^3

Marta Orselli; Troels Harmark

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Quantum Mechanical Sectors in Thermal N=4 Super Yang-Mills on RxS^3

Troels Harmark, Marta Orselli

High Energy Physics - Theory · Submitted 23 May 2006

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We find that when we are near a point with zero temperature and critical chemical potential, N=4 SYM on RxS^3 reduces to a quantum mechanical theory.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.19 · compares with prior results 0.15 · mentions code or data availability 0.01.

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We study the thermodynamics of U(N) N=4 Super Yang-Mills (SYM) on RxS^3 with non-zero chemical potentials for the SU(4) R-symmetry. We find that when we are near a point with zero temperature and critical chemical potential, N=4 SYM on RxS^3 reduces to a quantum mechanical theory. We identify three such critical regions giving rise to three different quantum mechanical theories. Two of them have a Hilbert space given by the SU(2) and SU(2|3) sectors of N=4 SYM of recent interest in the study of integrability, while the third one is the half-BPS sector dual to bubbling AdS geometries. In the planar limit the three quantum mechanical theories can be seen as spin chains. In particular, we identify a near-critical region in which N=4 SYM on RxS^3 essentially reduces to the ferromagnetic XXX_{1/2} Heisenberg spin chain. We find furthermore a limit in which this relation becomes exact.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study the thermodynamics of U(N) N=4 Super Yang-Mills (SYM) on RxS^3 with non-zero chemical potentials for the SU(4) R-symmetry.	contribution 0.92	0.89	0.05	asserted 0.93
s1	We find that when we are near a point with zero temperature and critical chemical potential, N=4 SYM on RxS^3 reduces to a quantum mechanical theory.	result 1.00	0.96	0.35	asserted 1.00
s2	We identify three such critical regions giving rise to three different quantum mechanical theories.	result 0.93	0.95	0.25	asserted 1.00
s3	Two of them have a Hilbert space given by the SU(2) and SU(2\|3) sectors of N=4 SYM of recent interest in the study of integrability, while the third one is the half-BPS sector dual to bubbling AdS geometries.	result 0.89	0.85	0.25	asserted 1.00
s4	In the planar limit the three quantum mechanical theories can be seen as spin chains.	result 0.65	0.78	0.14	asserted 0.73
s5	In particular, we identify a near-critical region in which N=4 SYM on RxS^3 essentially reduces to the ferromagnetic XXX_{1/2} Heisenberg spin chain.	result 0.98	0.93	0.26	asserted 0.93
s6	We find furthermore a limit in which this relation becomes exact.	result 0.99	0.93	0.13	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.96.

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Original abstract

We study the thermodynamics of U(N) N=4 Super Yang-Mills (SYM) on RxS^3 with non-zero chemical potentials for the SU(4) R-symmetry. We find that when we are near a point with zero temperature and critical chemical potential, N=4 SYM on RxS^3 reduces to a quantum mechanical theory. We identify three such critical regions giving rise to three different quantum mechanical theories. Two of them have a Hilbert space given by the SU(2) and SU(2|3) sectors of N=4 SYM of recent interest in the study of integrability, while the third one is the half-BPS sector dual to bubbling AdS geometries. In the planar limit the three quantum mechanical theories can be seen as spin chains. In particular, we identify a near-critical region in which N=4 SYM on RxS^3 essentially reduces to the ferromagnetic XXX_{1/2} Heisenberg spin chain. We find furthermore a limit in which this relation becomes exact.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Thermal Giant Graviton Expansion
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Exact finite-N and infinite-N expansions of free SYM partition functions are derived from chiral holography, with D-instantons resumming to the Hagedorn temperature.
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Twisted BPS decoupling limits of strings on AdS5 x S5 are defined as single-step limits, yielding non-relativistic sigma-models on symplectic U(1)-Galilean spaces, and extended to D-branes and to Spin Matrix theory limits.
Strings with Non-Relativistic Conformal Symmetry and Limits of the AdS/CFT Correspondence
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A Polyakov-type action for strings on torsional Newton-Cartan geometry is derived, its non-relativistic scaling limit is shown to carry a Galilean conformal algebra, and the limit is matched to Spin Matrix Theory limi...
Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence
hep-th 2014-09 conditional novelty 6.0 of 10

A new quantum mechanical matrix model reproduces N=4 super-Yang-Mills near zero-temperature critical points and, at high temperature, reduces to N^2+1 uncoupled harmonic oscillators, or 2N at infinite coupling.
The SU(2) x SU(2) sector in the string dual of N=6 superconformal Chern-Simons theory
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The authors derive the magnon dispersion relation in the SU(2)xSU(2) sector of the ABJM string dual and find it depends non-trivially on the coupling, unlike the analogous AdS5xS5 case.

How the literature uses it

29 arXiv papers cite this in 74 sentences

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Papers citing it · 45 sentences without a confident label

Builds on it 2 papers

We find a total of fourteen such decoupling limits of $=4$ SYM on $×S^3$, three of them found previously in [ref] .

Decoupling limits of N=4 super Yang-Mills on R x S^3 · Introduction · 0.85
[In [ref] the $𝔰𝔲(2)$ decoupling limit of [ref] is generalized to orbifolded $𝒩=2$ quiver gauge theory.]

Finite-size corrections to the rotating string and the winding state · Introduction · 0.87

Uses its method or tool 2 papers

Applying the approach of [ref] [See also [ref] for work on the winding state with the space-like isometry compactified.] to match the spectrum of operators and string states in the $SU(2)$ sector uses in an essential way the alternative Penrose limit of [ref] where the maximally supersymmetric pp-wave has an explicit isometry.

New Penrose Limits and AdS/CFT · Introduction · 0.86
At zero coupling $g=0$, the full refined partition function [ref] can be computed using Pólya theory [ref] : [equation] where $η_B(T,Ω_i)$ and $η_F(T,Ω_i)$ are the single-particle partition functions for the bosonic and fermionic modes on the three-sphere, computed for $=4$ SYM theory with chemical potentials in Refs. [ref] .

Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations · Zero-coupling limit and single-particle partition functions · 0.84

Compares with it 3 papers

Below we check our tree-level results that emerge from the TBA analysis with the previously derived results of Refs. [ref] using Pólya theory.

Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations · Zero-coupling limit and single-particle partition functions · 1.00
We find, in fact: (Ω_1,Ω_2,Ω_3) = (Ω, 0, 0): T_H=-1/log(1-Ω)[1-log(- log[1-Ω])/log(1-Ω)+…], (Ω_1,Ω_2,Ω_3) = (Ω, Ω, 0): T_H=1-Ω/log2[1-1/log2e^-log2/2(1-Ω)+𝒪(e^- log2/(1-Ω))], (Ω_1,Ω_2,Ω_3) = (Ω, Ω, Ω): T_H=1-Ω/log4[1-30/log4e^-2log4/(1-Ω)+𝒪(e^-3log4/(1-Ω))] , which have the same qualitative behavior of the analogous equations found in [ref] for the $𝒩=4$ theory.

Thermodynamics of theories with sixteen supercharges in non-trivial vacua · Chemical potentials · 1.00
It follows that [equation] The first line agrees with [ref] when $ξ=1, ω̃_1=0$, and with [ref] when $ξ=1$.[Note that (1.2) of [ref] is the Hagedorn temperature of the entire $=4$ SYM.

Refined Counting of Necklaces in One-loop $\mathcal{N}=4$ SYM · Hagedorn temperature · 1.00

Cites it as background 12 papers

We consider the following decoupling limit of $SU(N)$ $=4$ SYM on $×S^3$ [ref]

Matching gauge theory and string theory in a decoupling limit of AdS/CFT · The $SU(2)$ decoupling limit of $=4$ SYM on $×S^3$ · 0.80
The conjectured duality between the quantum mechanical/ Spin-Matrix theory (SMT) limit [ref] - [ref] of $𝒩=4$ SYM and the nonrelativistic strings [ref] - [ref] propagating in $AdS_5 ×S^5$ [ref] - [ref] has opened up a new era in the context of nonrelativstic gauge/string duality.

Multispin magnons from Spin-Matrix strings on $ AdS_5 \times S^5 $ · Overview and Motivation · 0.97
During last one decade, a series of work [ref] - [ref] have been put forward which essentially argues about a more tractable limit of the AdS$_5$/CFT$_4$ correspondence [ref] - [ref] in a regime, [equation] where both the descriptions are under control and hence the corresponding spectrum could be subjected to a precise test.

Nonrelativistic spinning strings · Spin-Matrix theory and NR strings · 0.82

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