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Open spin chains for giant gravitons and relativity
High Energy Physics - Theory · Submitted 10 May 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This provides evidence for ten dimensional local physics mixing AdS directions and the five-sphere emerging from an N=4 SYM computation in the presence of a non-trivial background (made of D-branes) that break the conformal field theory of the system.
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The abstract, sentence by sentence
We study open spin chains for strings stretched between giant graviton states in the N=4 SYM field theory in the collective coordinate approach. We study the boundary conditions and the effective Hamiltonian of the corresponding spin chain to two loop order. The ground states of the spin chain have energies that match the relativistic dispersion relation characteristic of massive W boson particles on the worldvolume of the giant graviton configurations, up to second order in the limit where the momentum is much larger than the mass. We find evidence for a non-renormalization theorem for the ground state wave function of this spin chain system. We also conjecture a generalization of this result to all loop orders which makes it compatible with a fully relativistic dispersion relation. We show that the conjecture follows if one assumes that the spin chain admits a central charge extension that is sourced by the giant gravitons, generalizing the giant magnon dispersion relation for closed string excitations. This provides evidence for ten dimensional local physics mixing AdS directions and the five-sphere emerging from an N=4 SYM computation in the presence of a non-trivial background (made of D-branes) that break the conformal field theory of the system.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study open spin chains for strings stretched between giant graviton states in the N=4 SYM field theory in the collective coordinate approach. | contribution 0.98 | 0.93 | 0.04 | asserted 0.95 |
| s1 | We study the boundary conditions and the effective Hamiltonian of the corresponding spin chain to two loop order. | contribution 0.94 | 0.95 | 0.04 | asserted 0.95 |
| s2 | The ground states of the spin chain have energies that match the relativistic dispersion relation characteristic of massive W boson particles on the worldvolume of the giant graviton configurations, up to second order in the limit where the momentum is much larger than the mass. | result 0.99 | 0.92 | 0.52 | asserted 0.99 |
| s3 | We find evidence for a non-renormalization theorem for the ground state wave function of this spin chain system. | result 0.99 | 0.95 | 0.13 | asserted 0.56 |
| s4 | We also conjecture a generalization of this result to all loop orders which makes it compatible with a fully relativistic dispersion relation. | contribution 0.52 | 0.77 | 0.24 | speculative 0.99 |
| s5 | We show that the conjecture follows if one assumes that the spin chain admits a central charge extension that is sourced by the giant gravitons, generalizing the giant magnon dispersion relation for closed string excitations. | result 0.39 | 0.83 | 0.19 | asserted 0.88 |
| s6 | This provides evidence for ten dimensional local physics mixing AdS directions and the five-sphere emerging from an N=4 SYM computation in the presence of a non-trivial background (made of D-branes) that break the conformal field theory of the system. | interpretation 0.99 | 0.79 | 0.39 | hedged possibility 0.66 |
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The paper
Original abstract
We study open spin chains for strings stretched between giant graviton states in the N=4 SYM field theory in the collective coordinate approach. We study the boundary conditions and the effective Hamiltonian of the corresponding spin chain to two loop order. The ground states of the spin chain have energies that match the relativistic dispersion relation characteristic of massive W boson particles on the worldvolume of the giant graviton configurations, up to second order in the limit where the momentum is much larger than the mass. We find evidence for a non-renormalization theorem for the ground state wave function of this spin chain system. We also conjecture a generalization of this result to all loop orders which makes it compatible with a fully relativistic dispersion relation. We show that the conjecture follows if one assumes that the spin chain admits a central charge extension that is sourced by the giant gravitons, generalizing the giant magnon dispersion relation for closed string excitations. This provides evidence for ten dimensional local physics mixing AdS directions and the five-sphere emerging from an N=4 SYM computation in the presence of a non-trivial background (made of D-branes) that break the conformal field theory of the system.
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References
How the literature uses it
23 arXiv papers cite this in 44 sentences
Papers citing it · 34 sentences without a confident label
Builds on it 1 paper
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We work with open string states constructed in the $$ sector of the gauge theory, continuing the work of [ref] .
Excited States of Open Strings From $\mathcal{N}=4$ SYM · Introduction · 1.00
Uses its method or tool 2 papers
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To add the boundary conditions, we follow the calculations in [ref] .
Giant gravitons and the emergence of geometric limits in $\beta$-deformations of ${\cal N}=4$ SYM · The $β$-deformed spin chain with boundaries · 0.99
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Here, I will follow the results in [ref] to describe how the spectrum of strings stretching between giant gravitons is geometric in the collective coordinates we found above.
Sketches of emergent geometry in the gauge/gravity duality · Cuntz oscillators and strings · 0.84
Compares with it 2 papers
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The result agrees with explicit one loop computations in [ref] , two loop computations in [ref] and even three loop computations performed in [ref] using a collective coordinate [ref] approach.
Interacting Double Coset Magnons · Introduction · 0.88
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Note that [ref] is not using the language of the double coset ansatz, but instead employs a collective coordinate approach [ref] which is well suited to the semi-classical limit.
Central Charges for the Double Coset · Introduction · 0.83
Cites it as background 5 papers
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In the second viewpoint, we study the open string as a classical integrable system [ref] , or a boundary integrable system [ref] .[A coherent state description of open strings ending on a mixture of (generally non-maximal) giant gravitons is studied in [ref] .] In both points of view, the brane-string system typically has divergent energy, which is canceled by a divergent angular momentum of open strings, just like the giant magnon [ref] .
Oscillating Multiple Giants · Introduction · 0.88
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These bases have been useful for exploring giant gravitons [ref] and new background geometries [ref] in AdS/CFT [ref] , as well as for the computations of anomalous dimensions in large $N$ but non-planar limits [ref] .
Finite N Quiver Gauge Theory · Summary and Conclusions · 0.87
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The Cuntz oscillators appear repeatedly also in the study of open spin chain dual states to open strings in the AdS/CFT correspondence [ref] and their coherent states are especially important to describe the ground state energies of the corresponding open spin chains [ref] .
Superposition induced topology changes in quantum gravity · Physical Interpretations · 0.89
What it cites · 26 sentences without a confident label
Builds on 1 paper
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The present paper utilizes this new collective coordinate approach to compute the open spin chain boundary conditions for strings stretched between giant gravitons in the $SU(2)$ sector, generalizing previous results [ref] .
Giant magnon bound states from strongly coupled N=4 SYM · Introduction · 0.98
Compares with 1 paper
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First, when $k=0$ (a chain with no sites), we reproduce the energy of the configurations calculated in [ref] , to show that we have consistency with the previous evaluation using the collective coordinate method.
Giant gravitons: a collective coordinate approach · Ground State for Open Spin Chain and Geometric Interpretation · 0.99
Cites as support 3 papers
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One can make other field theory arguments that suggest that this is the only result that is compatible with S-duality [ref]
S-duality and the giant magnon dispersion relation · Higher Loops and a Relativistic Dispersion Relation · 0.98
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Although we have not studied this process yet, the fact that there is an effective gauge theory on giant graviton states is understood because one can see that there is a Gauss' law constraint for counting string states between giants [ref] (see also [ref] ).
A double coset ansatz for integrability in AdS/CFT · Conclusion · 0.97
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Although we have not studied this process yet, the fact that there is an effective gauge theory on giant graviton states is understood because one can see that there is a Gauss' law constraint for counting string states between giants [ref] (see also [ref] ).
Giant gravitons: a collective coordinate approach · Conclusion · 0.97
Cites as background 1 paper
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A review of this program can be found in [ref] .
Review of AdS/CFT Integrability: An Overview · The Cuntz Hamiltonian at Two Loops · 0.99
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