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Three Roads to Probe-Brane Superconductivity
High Energy Physics - Theory · Submitted 23 Nov 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Comparing these phases first in the \alpha'^2 expansion, we find that the internal scalar has the largest critical temperature and is always thermodynamically preferred.
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The abstract, sentence by sentence
We study a defect system of two parallel D5 probe branes in a large-N_c D3 background. Using the non-abelian DBI action, we study three different fields that can give rise to a superconducting phase transition: A vector (p-wave), a scalar corresponding to a non-trivial "separation"' of the branes in the (3+1) field theory directions and a scalar corresponding to a separation in the "internal" S^5 (both s-wave). Comparing these phases first in the \alpha'^2 expansion, we find that the internal scalar has the largest critical temperature and is always thermodynamically preferred. Further, there is an interesting attractor behavior. Taking a simplified version of the full DBI action that preserves its regularity and geometry, we find that the divergences of the \alpha'^2 expansion are resolved and some second order transitions turn into first order ones. In addition to some other changes of the phase diagram due to the structure of the DBI action, we observe that the ground state degeneracy of the unbroken theory is lifted. We also isolate the unphysical artifacts of our simplification.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study a defect system of two parallel D5 probe branes in a large-N_c D3 background. | contribution 0.66 | 0.74 | 0.02 | asserted 0.94 |
| s1 | Using the non-abelian DBI action, we study three different fields that can give rise to a superconducting phase transition: A vector (p-wave), a scalar corresponding to a non-trivial "separation"' of the branes in the (3+1) field theory directions and a scalar corresponding to a separation in the "internal" S^5 (both s-wave). | contribution 0.81 | 0.94 | 0.07 | asserted 0.90 |
| s2 | Comparing these phases first in the \alpha'^2 expansion, we find that the internal scalar has the largest critical temperature and is always thermodynamically preferred. | result 1.00 | 0.96 | 0.50 | asserted 1.00 |
| s3 | Further, there is an interesting attractor behavior. | result 0.97 | 0.63 | 0.04 | asserted 0.88 |
| s4 | Taking a simplified version of the full DBI action that preserves its regularity and geometry, we find that the divergences of the \alpha'^2 expansion are resolved and some second order transitions turn into first order ones. | result 0.83 | 0.97 | 0.15 | asserted 1.00 |
| s5 | In addition to some other changes of the phase diagram due to the structure of the DBI action, we observe that the ground state degeneracy of the unbroken theory is lifted. | result 1.00 | 0.94 | 0.13 | asserted 1.00 |
| s6 | We also isolate the unphysical artifacts of our simplification. | limitation 0.68 | 0.94 | 0.04 | asserted 0.98 |
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The paper
Original abstract
We study a defect system of two parallel D5 probe branes in a large-N_c D3 background. Using the non-abelian DBI action, we study three different fields that can give rise to a superconducting phase transition: A vector (p-wave), a scalar corresponding to a non-trivial "separation"' of the branes in the (3+1) field theory directions and a scalar corresponding to a separation in the "internal" S^5 (both s-wave). Comparing these phases first in the \alpha'^2 expansion, we find that the internal scalar has the largest critical temperature and is always thermodynamically preferred. Further, there is an interesting attractor behavior. Taking a simplified version of the full DBI action that preserves its regularity and geometry, we find that the divergences of the \alpha'^2 expansion are resolved and some second order transitions turn into first order ones. In addition to some other changes of the phase diagram due to the structure of the DBI action, we observe that the ground state degeneracy of the unbroken theory is lifted. We also isolate the unphysical artifacts of our simplification.
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How the literature uses it
3 arXiv papers cite this in 3 sentences
Papers citing it · 2 sentences without a confident label
Cites it as background 1 paper
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In [ref] the D3/D5 system, constructed to be a defect theory, was used to study different condensates corresponding to vector/scalar modes on the flavor D5 brane worldvolume.
1+1-dimensional p-wave superconductors from intersecting D-branes · Introduction · 0.91
What it cites · 42 sentences without a confident label
Uses the method or tool of 2 papers
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By studying the variation of the fields, one can trivially see that this is actually a function of the chemical potential, rather than the density, so we get [ref] : [equation] The counter terms that we need to add are dictated to us by requiring consistency of the variational principle and give in analogy to the abelian case [ref] [equation] As we will see later, it turns out that the other scalar $ψ$ does not contribute to the boundary term.
Holographic phase transitions at finite chemical potential · Setup · 0.92
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By studying the variation of the fields, one can trivially see that this is actually a function of the chemical potential, rather than the density, so we get [ref] : [equation] The counter terms that we need to add are dictated to us by requiring consistency of the variational principle and give in analogy to the abelian case [ref] [equation] As we will see later, it turns out that the other scalar $ψ$ does not contribute to the boundary term.
Thermodynamics of Holographic Defects · Setup · 0.92
Compares with 3 papers
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These features are reminiscent of the meson melting phase transition [ref] and its many aspects/relatives in different regimes (see e.g. [ref] ).
Thermodynamics of Holographic Defects · Combined Results · 0.87
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These features are reminiscent of the meson melting phase transition [ref] and its many aspects/relatives in different regimes (see e.g. [ref] ).
Holographic Berezinskii-Kosterlitz-Thouless Transitions · Combined Results · 0.87
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These features are reminiscent of the meson melting phase transition [ref] and its many aspects/relatives in different regimes (see e.g. [ref] ).
Phase diagram of the D3/D5 system in a magnetic field and a BKT transition · Combined Results · 0.87
Cites as background 26 papers
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As we discussed in section [ref], we have two scalars at hand that we can use for the symmetry breaking, the one corresponding to the separation of the probe branes in the $z$ direction along the D3 branes, and the one on the sphere separating the probe branes from the D3's, corresponding in the usual picture to a finite quark mass [ref] or chiral symmetry breaking [ref] .
Phase diagram of the D3/D5 system in a magnetic field and a BKT transition · Flat scalar · 0.95
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As we discussed in section [ref], we have two scalars at hand that we can use for the symmetry breaking, the one corresponding to the separation of the probe branes in the $z$ direction along the D3 branes, and the one on the sphere separating the probe branes from the D3's, corresponding in the usual picture to a finite quark mass [ref] or chiral symmetry breaking [ref] .
Holographic phase transitions at finite chemical potential · Flat scalar · 0.95
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As we discussed in section [ref], we have two scalars at hand that we can use for the symmetry breaking, the one corresponding to the separation of the probe branes in the $z$ direction along the D3 branes, and the one on the sphere separating the probe branes from the D3's, corresponding in the usual picture to a finite quark mass [ref] or chiral symmetry breaking [ref] .
Holographic Experiments on Defects · Flat scalar · 0.95
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