Semi-superfluid strings in High Density QCD

A. P. Balachandran; S. Digal; T. Matsuura

REVIEW

Semi-superfluid strings in High Density QCD

A. P. Balachandran, S. Digal, T. Matsuura

High Energy Physics - Phenomenology · Submitted 26 Sep 2005 · 23 references

Pith's verdict: The homotopy classification is right and the mixed flux quantization is a real new ingredient; the 'only stable strings' line outruns what they actually computed.

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arXiv IDhep-ph/0509276 (version 3)

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CitationA. P. Balachandran, S. Digal, T. Matsuura. "Semi-superfluid strings in High Density QCD." arXiv:hep-ph/0509276 (2005). https://pith.science/paper/ESZ6QTLM

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Worth your time if you work on CFL defects or compact-star matter, with one caveat about how far the headline goes. The core result is clean: the CFL order parameter space is U(3), π1 = Z, and the loops that combine a color rotation with a baryon-number rotation give strings distinct from the abelian vortices of Forbes-Zhitnitsky and Iida-Baym and from Iida's non-topological A_X flux tube. That classification is standard homotopy done correctly, and importing the Balachandran-Digal non-abelian defect machinery into color superconductivity is a sensible move rather than a repackaging. The mixed flux quantization condition, Eq. 16, with the A_EM–A_8 mixing feeding both ordinary and color magnetic flux, is the genuinely new piece and it is derived, not asserted. The reduction of the gradient energy by 1/3 for the l loop versus 2/3 for l' is a nice concrete check that the two loops really are dynamically different despite being topologically the same projection in SU(3). The numerical section is honest about its own shortcut: ψ1,2 = η is frozen, and the paper says the true minimum has r-dependent profiles. That weakens the quoted configurations and energies but not the existence argument, and they flag it themselves. Two things I would push on in review. First, Section IV's claim that these are 'the only stable topological string solutions' mixes a topological statement (the A_X tube is trivial in π1, which is correct) with a dynamical one (it is unstable, argued by analogy to electroweak strings). Electroweak-string stability depends on m_H/m_Z, not just g > e, so the analogy is suggestive but not a computation. Second, the paper itself says 'It is not clear if one of these configuration decays into the other... We address this issue in a future work' — the decay of the non-abelian string into the l³/abelian configuration is left open, and that is the load-bearing stability question. Minor: the stated ᾱ = 8βη² has the wrong sign for a symmetry-breaking minimum; it should be negative, and the equations below it clearly assume that, so it reads as a typo. The Section IV network scenario is speculative and labelled as such. Send it out; the topology is solid and the open stability question is worth a referee's attention.

Referee report

Significance

If the identification is correct, the stable topological defects of CFL matter are non-abelian semi-superfluid strings rather than the abelian superfluid vortices of refs. [8,9] or the non-topological A_X flux tubes of ref. [10]. That would be a genuine and useful contribution to the physics of dense quark matter, and the astrophysical scenario, while speculative, is a reasonable first pass at the observational consequences. The homotopy argument (OPS = U(3), π1 = Z, loops l and l') is sound and the GL treatment is an appropriate first step. The paper does not ship machine-checked proofs or reproducible code, and the numerical section is not a parameter-free derivation; the strengths here are the topological classification and the identification of the correct gauge-field mixing in the string ansatz.

Major objections (4)

[Section IV, first paragraph] The sentence 'Our non-abelian string solutions are the only stable topological string solutions with quantized flux of ordinary as well as color magnetic field' asserts stability that the paper does not compute. Section III explicitly leaves the decay question open: 'It is not clear if one of these configuration decays into the other. We address this issue in a future work.' The non-abelian string is topologically equivalent both to the l^3 abelian superfluid vortex and to three elementary non-abelian strings, so whether the M1 configuration is a local minimum of the GL energy is a dynamical question that requires a fluctuation analysis or an explicit energy comparison at the stated parameters. The abstract's existence claim is topological and survives, but the word 'stable' in Section IV should either be supported by such a calculation or removed.
[Section II, paragraph discussing ref. [10]] The A_X flux tube of ref. [10] is declared unstable 'because the strong coupling constant is an order of magnitude larger than the electromagnetic coupling.' In the electroweak case the stability of the Z-string depends on m_H/m_Z (and on sin^2 θ_W), not merely on g > e, so the analogy is heuristic. The paper's own parameters give m_A ≈ 183 MeV and a Higgs mass of the same order, so the actual ratio is in a regime where the electroweak analogy is not decisive. A concrete stability criterion, or at least a fluctuation spectrum for the A_X string in the CFL GL theory, is needed before the competing solution can be dismissed.
[Section III, after Eq. (17)] The numerical solutions freeze the non-winding components at ψ1,2(r) = η, and the paper acknowledges that 'the string configuration with the lowest energy will have some r dependent profile for ψ1,2(r).' The abstract nevertheless states 'we find the configurations of these strings,' and the comparison between the l and l' profiles in Figs. 1 and 2 is presented as a physical energy comparison. Because the true minimum has r-dependent ψ1,2, the quoted profiles and the relative energies are not the true minimum-energy configurations. The qualitative conclusion that l' costs more gradient energy in U(1)_B is robust, but the quantitative energy comparison should be softened or the full coupled system should be solved.
[Section II, final paragraph] The statement that 'one will not have any stable topological string solution in the 2SC and g2SC phases' appears to contradict the paper's own introduction, which states that superfluid vortices are topologically stable and cites ref. [11] for the 2SC phase. In 2SC the diquark condensate carries baryon number, so U(1)_B is spontaneously broken and abelian superfluid vortices should exist. The claim should be restricted to non-abelian strings, or the triviality of the relevant loops in 2SC should be demonstrated explicitly.

Minor objections (10)

[Section I, final paragraph] The sentence 'In Section IV, we present our conclusions' should refer to Section V; the conclusions are in Section V.
[Section III, text after Eq. (35)] The relation ᾱ = 8βη² should carry a minus sign: Eq. (25) admits f = 1 as a solution only for ᾱ = -8βη². The same sign should be corrected in Eq. (35) and in the numerical value quoted in the text.
[Section III, text after Eq. (35)] The quoted Higgs mass m_Φ ≈ 245 MeV should be derived explicitly. With the kinetic normalization 2κ_T of Eq. (18), the curvature of the potential at the minimum gives m_Φ² = 8βη²/κ_T, which is four times the value implied by the quoted number; the Meissner mass m_A² = 2κ_T g_x²η² does reproduce 183 MeV. The type-II conclusion is unaffected, but the numbers should be consistent.
[Eq. (32)] The last term, '16 g_x² η² / 9 A_μ', appears to be missing a factor of κ_T when compared with the corresponding term in Eq. (24).
[Eqs. (24) and (32)] These equations are written in a Cartesian-looking form, but the non-zero component is A_θ in polar coordinates, which carries explicit 1/r factors. As printed, the current term does not transparently reduce to the source term in Eqs. (26) and (34); please state the coordinate convention explicitly.
[Eq. (2)] Φ carries the anti-fundamental of color, so the color covariant derivative should act with -(T^a)^T on the right rather than with T^a on the left. For the diagonal ansatz used in Section III this makes no difference, but the notation should be corrected for the general case.
[Section III, after Eqs. (21) and (30)] The phrase 'reduces the gradient energy by 1/3' should read 'to 1/3' (or 'by a factor of 3'), and 'only by a factor of 2/3' should read 'only to 2/3'; as written the two statements are ambiguous about whether the reduction is multiplicative or subtractive.
[Eq. (18)] The potential is written with a single β, which implicitly sets β1 = β2 ≡ β in Eq. (1). This choice should be stated explicitly, since the numerical results depend on it.
[Figs. 1 and 2] The axis labels and units should be legible in the published version, and the asymptotic values and core radii would be easier to read if marked on the plots. A short table of the energy per unit length for the two loops at the stated parameters would make the comparison in Section III quantitative.
[Section II, paragraph on gCFL] The statement that 'in the gCFL phase also there will be semi-superfluid strings since the symmetry breaking pattern and the OPS are same as that of CFL case' is presented as an expectation; it should be flagged as such, or supported by the corresponding loop argument.

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The paper

The paper claims

Color-superconducting star cores could host stable non-abelian strings, not just ordinary vortices.

The reading

The paper asks what kinds of stable line-like defects — vortices or flux tubes — can exist in the color-flavor locked (CFL) phase of dense quark matter, the state expected at the core of very dense stars. Earlier work looked only at loops in the order-parameter space generated by baryon number, giving ordinary superfluid vortices, or at a flux tube of the massive mixed gauge field, which the authors argue is not topologically protected and is unstable for realistic couplings. The authors point out that the order-parameter space is $U(3)$, whose first homotopy group is $Z$, and that its generator is a loop that winds partly in color and partly in baryon number; because the photon and the eighth gluon mix in CFL, the minimum-energy string must carry both ordinary and color magnetic flux, with $(e/2)(e$-flux) $+ (g/2)(g$-flux) $= 2.2$ units of the massive field's flux. They then solve the Ginzburg-Landau equations numerically for two representative loops and describe how such a string network could form and evolve during the cooling transition at a star's core. If the picture holds, the stable defects of CFL matter are a distinct hybrid object: a superfluid vortex whose energy per unit length grows only logarithmically with system size, but which also carries quantized magnetic flux.

What carries the argument

The load-bearing object is the order-parameter space $U(3)$ and its first homotopy group $Z$, combined with the gauge-field mixing of CFL. A closed loop in $U(3)$ can be realized as a path in $SU(3) . U(1)_B$ that closes only after quotienting by $Z_3 . Z_3$; the elementary non-abelian string corresponds to the generator $[l]$, while $[l]^3$ reduces to the ordinary abelian superfluid vortex and $[l]^2$ gives the oppositely oriented partner. The mixing angle $..$ with $..s.. = .(e^2/(e^2 + 3g^2/4))$ determines how the winding is shared between ordinary and color magnetic flux; the minimum-energy configuration distributes it so that only the massive combination $A_X$ is excited. The Ginzburg-Landau free energy with covariant derivatives built from $A_{EM}$ and $A_8$ then supplies the two coupled radial equations for $f(r)$ and $.(r)$ that the paper integrates numerically.

Extended reading notes

Core claim

The central claim is that the CFL phase supports topological strings that are simultaneously superfluid vortices and magnetic flux tubes. The argument runs through the order-parameter space: the diquark condensate $f$ is a $3.2$ matrix, the symmetry breaking pattern $[SU(3)_C . SU(3)_F . U(1)_B]/[SU(3) . Z_3]$ leaves $U(3)$ as the space of degenerate ground states, and $Z_1(U(3)) = Z$. The generator of that $Z$ is a loop that returns to the identity only after a simultaneous rotation by $e^{2.2i/3}$ in the color-flavor part and $e^{-2.2i/3}$ in the baryon-number part. Because the photon $A_{EM}$ and the gluon $A_8$ mix into a massive field $A_X$ and a massless field $A_Q$, the lowest-energy string excites only $A_X$, and its flux is quantized by $g_x = .(e^2 + 3g^2/4)$, giving $(e/2)(e$-flux) $+ (g/2)(g$-flux) $= 2.2$. Solving the coupled equations for the winding condensate component $f(r)$ and the gauge profile $.(r)$ with $g_x = 2.0$, $._T = 0.42$, $._1 = 1.26$ and $. = 100$ MeV (Higgs mass about 245 MeV, Meissner mass about 183 MeV), the authors find profiles that approach their asymptotic values more slowly for the loop that travels the longer path in $U(1)_B$, and correspondingly cost more gradient energy. The energy per unit length remains logarithmically divergent with system size — hence 'semi-superfluid' — which the authors argue is acceptable for a finite star even though it would rule the string out as an infinite-system defect.

Load-bearing premise

The numerical string profiles and energies are computed with the non-winding condensate components frozen at their asymptotic value, an approximation the authors state explicitly, so the quoted configurations are not the true minimum-energy solutions even though the topological existence argument does not depend on it.

Editorial extensions

If this is right

The stable defects of CFL matter are non-abelian semi-superfluid strings carrying quantized ordinary and color magnetic flux, not the abelian vortices or the non-topological $A_X$ flux tube studied earlier.
Because the string core is not color-flavor locked while the exterior is, the defect marks a localized region where the locked phase is restored.
An electron transported around such a string picks up an Aharonov-Bohm phase different from $2.2$, so electrons should scatter strongly off these strings.
During a first-order QGP-to-CFL transition at a stellar core, the Kibble mechanism can leave a network of these strings; only radially oriented ones survive the inward march of the CFL shell, and pairing of opposite-winding strings into V-shaped configurations can feed back on the star's angular momentum.
The same non-abelian loops persist in the mCFL, dSC, uSC and gCFL phases, while in 2SC and g2SC the baryon-number and $T_8$ loops coincide and no stable topological string survives.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The logarithmic energy divergence means the defect's tension depends on the size of the host star, so any observational signature — say, a strain or a transport anomaly tied to string density — would be sensitive to stellar radius rather than being a fixed material constant.
If the strings really dominate the defect population, then the superfluid rotation of a CFL core cannot be carried by ordinary abelian vortices alone; the critical spin-up rate at which vortices are forced into the core should be set by the non-abelian string tension instead.
A useful cross-check would be to ask whether the same $U(3)$ loop analysis constrains the confinement-to-CFL interface: the paper allows strings to terminate on color monopole pairs in the surrounding confined matter, which suggests a direct link between defect density and the monopole population of the crust.
The strong electron scattering the authors mention is, in principle, a transport signature: a dense string network in a CFL core would add a scattering channel that could show up in the star's cooling curve, though the paper does not estimate the size of the effect.

Original abstract

We show that topological superfluid strings/vortices with flux tubes exist in the color-flavor locked (CFL) phase of color superconductors. Using a Ginzburg-Landau free energy we find the configurations of these strings. These strings can form during the transition from the normal phase to the CFL phase at the core of very dense stars. We discuss an interesting scenario for a network of strings and its evolution at the core of dense stars.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We show that topological superfluid strings/vortices with flux tubes exist in the color-flavor locked (CFL) phase of color superconductors. Using a Ginzburg-Landau free energy we find the configurations of these strings. These strings can form during the transition from the normal phase to the CFL phase at the core of very dense stars. We discuss an interesting scenario for a network of strings and its evolution at the core of dense stars.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We show that topological superfluid strings/vortices with flux tubes exist in the color-flavor locked (CFL) phase of color superconductors.	result 0.72	0.90	0.83	asserted 1.00
s1	Using a Ginzburg-Landau free energy we find the configurations of these strings.	method 0.98	0.95	0.07	asserted 1.00
s2	These strings can form during the transition from the normal phase to the CFL phase at the core of very dense stars.	interpretation 0.55	0.45	0.16	hedged possibility 0.83
s3	We discuss an interesting scenario for a network of strings and its evolution at the core of dense stars.	contribution 0.71	0.65	0.12	asserted 0.52

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.97.

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sources read

arXiv listing abstract v3

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full text
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (23)

[10]

K. Iida, Phys. Rev. D 71, 054011(2005)

View on Pith 2005
[11]

D. Blaschke and D. Sedrakian, nucl-th/0006038

View on Pith Pith review arXiv
[1]

D. Bailin and A. Love, Phys. Rep. 107, 325 (1984); M. Iwasaki and T. Iwado, Phys. Lett. B 350, 163 (1995); M. Alford, K. Rajagopal, and F. Wilczek, Phys. Lett. B 422, 247 (1998); R. Rapp, T. Sch¨ afer, 12 E.V. Shuryak, and M. Velkovsky, Phys. Rev. Lett. 81, 53 (1998)

View on Pith 1984
[2]

K. Iida, T. Matsuura, M. Tachibana and T. Hatsuda, Phys. R ev. Lett. 93, 132001 (2004); ibid Phys. Rev. D 71, 054003 (2005)

View on Pith 2004
[3]

S.B. Ruster, I.A. Shovkovy, and D.H. Rischke, Nucl. Phys . A743, 127 (2004); K. Fukushima, C. Kou- varis, and K. Rajagopal, Phys. Rev. D 71, 034002(2005)

View on Pith 2004
[4]

M. Alford, C. Kouvaris and K. Rajagopal, Phys. Rev. Lett. 92, 222001 (2004); Phys. Rev. D 71, 054009 (2005)

View on Pith 2004
[5]

M. Huang and I. Shovkovy, Phys. Lett. B 564, 205 (2003); Nucl. Phys. A729, 835 (2003)

View on Pith 2003
[6]

A. I. Larkin and Yu. N. Ovchinnikov, Sov. Phys. JETP 20, 762 (1965); P. Fulde and R. A. Ferrell, Phys. Rev. 135, A550 (1964)

View on Pith 1965
[7]

M. G. Alford, J. A. Bowers and K. Rajagopal, Phys. Rev. D 63, 074016 (2001)

View on Pith 2001
[8]

M. M. Forbes and A. R. Zhitnisky, Phys. Rev. D 65, 085009(2002)

View on Pith 2002
[9]

K. Iida and G. Baym, Phys. Rev. D 66, 014015 (2002)

View on Pith 2002
[12]

A. P. Balachandran, G. Marmo, N. Mukunda, J. S. Nilsson, E. C. G. Sudarshan, and F. Zaccaria, Phys. Rev. Lett 50, 1553 (1983); ibid Phys. Rev. D 29, 2919 (1984); ibid Phys. Rev. D 29, 2936 (1984); A. Abouelsaood, Phys. Lett. B 125, 467 (1983) and references therein

View on Pith 1983
[13]

A. P. Balachandran and S. Digal, Int. J. Mod. Phys. A 17, 1149 (2002); A. P. Balachandran and S. Digal, Phys. Rev. D 66, 034018 (2002)

View on Pith 2002
[14]

I. Giannakis and H. Ren, Nucl. Phys. B669, 462(2003)

View on Pith 2003
[15]

I. Giannakis and H. Ren, Phys. Rev. D 65, 054017

View on Pith
[16]

M. G. Alford, K. Rajagopal and F. Wilczek, Nucl. Phys. B537, 443(1999)

View on Pith 1999
[17]

K. Iida and G. Baym, Phys. Rev. D 63, 074018 (2001); ibid. 66, 059903(E) (2002)

View on Pith 2001
[18]

M. James, L. Perivolaropoulos, T. Vachaspati, Nucl. Ph ys. B395, 534(1993)

View on Pith 1993
[19]

T. W. B. Kibble, J. Phys. A 9:1387-1398, (1976)

View on Pith 1976
[20]

S. Rudaz, A. M. Srivastava and S. Verma, Int. J. Mod. Phys . A 14, 1591(1999)

View on Pith 1999
[21]

M. Hindmarsch, A. Davis and R. H. Brandenberger, Phys. R ev. D 49, 1944 (1994)

View on Pith 1994
[22]

S. Digal, A. M. Srivastava, Phys. Rev. Lett. 76:583-586,(1996); S. Digal, S. Sengupta, and A. M. Srivastava, Phys. Rev. D 58:103510,(1998)

View on Pith 1996
[23]

M. G. Alford, J. Berges and K. Rajagopal, Nucl. Phys. B571, 269(2000)

View on Pith 2000

Forward citations

Cited by 14 Pith papers

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

Fractional Superfluid Vortices and Worldsheet Wess--Zumino--Witten Models in Two-Color QCD and $Sp(2N)$ Gauge Theories
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Minimal superfluid vortices in even-flavor pseudoreal gauge theories wind only 1/m of the baryon circulation quantum and localize Sp(2m)_N WZW conformal field theories with central charge Nm(2m+1)/(N+m+1).
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hep-th 2018-08 accept novelty 7.0 of 10

High-density color-flavor-locked quark matter hosts Z3-valued particle-vortex braiding and one-third-quantized orbital angular momentum, which would rule out a smooth quark-hadron continuity.
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hep-th 2026-10 accept novelty 6.0 of 10

At equal mass scales, order-three A4 vortices are linearly stable while an order-two vortex has an exact negative mode, proving that restricted Bogomol'nyi structure does not imply full stability.
Quark-hadron continuity beyond Ginzburg-Landau paradigm
hep-th 2018-11 conditional novelty 6.0 of 10

The color-flavor locked phase of dense quark matter has no deconfined topological order, so a continuous connection to nuclear superfluid matter remains consistent.

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Non-Abelian Strings in High Density QCD: Zero Modes and Interactions
hep-ph 2007-08 conditional novelty 6.0 of 10

Non-Abelian semi-superfluid strings in color superconductivity have normalizable orientational zero modes and universally repel, making U(1)_B superfluid vortices unstable.
Continuity of vortices from the hadronic to the color-flavor locked phase in dense matter
hep-ph 2018-03 conditional novelty 5.0 of 10

A singly quantized vortex in three-flavor hadronic matter matches a singly quantized non-Abelian vortex in color-flavor locked quark matter in both circulation and angular momentum, so the two can connect without a boojum.
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The paper proposes that chiral gravitational waves generate both visible and dark baryon asymmetries via the gravitational anomaly, with dark quarks condensing into a superfluid whose Higgs mode is cold dark matter.
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An explicit ansatz for a neutral bion in the CP^{N-1} model reproduces the exponential slope and 1/N prefactor scaling of the far-separated instanton calculus, up to a 2 pi normalization factor.
Color Magnetic Flux Tubes in Dense QCD. II: Effective World-Sheet Theory
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Orientational zero modes of non-Abelian superfluid vortices in the color-flavor-locked phase are normalizable, and their world-sheet dynamics is a CP^2 sigma model with a numerically computed Kähler class.
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How the literature uses it

46 arXiv papers cite this in 71 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 53 sentences without a confident label

Compares with it 1 paper

This situation is quite similar to a non-Abelian vortex in dense QCD [ref] , see Ref. [ref] as a review.

Dynamics of Nambu monopole in two Higgs doublet models -- Cosmological Monopole Collider -- · Asymptotics of $Z$ strings · 0.81

Cites it as support 1 paper

This vortex can be continuously connected to a non-Abelian CFL vortex [ref] in the CFL quark phase (lower half of the figure) where the vortex has the same baryon circulation, but it arises in the unitary gauge from three diquark condensates, one of which acquires a phase of $2π$ when transported around the core.

Continuity of vortices from the hadronic to the color-flavor locked phase in dense matter · Introduction · 0.98

Cites it as background 16 papers

The existence of non-Abelian global strings was first pointed out by Balachandran and Digal in a seminal paper [ref] [ Non-Abelian global strings with $SU(N)_L$ gauged appear in high density QCD [ref] .

Non-Abelian Global Strings at Chiral Phase Transition · Introduction · 0.90
Minimal circulation vortex configurations in high density quark matter were first examined in Ref. [ref] .

Anyonic particle-vortex statistics and the nature of dense quark matter · Vortices in dense quark matter · 0.96
The most fundamental objects are non-Abelian vortices carrying color magnetic fluxes [ref] , which were called the semi-superfluid vortices.

Color Magnetic Flux Tubes in Dense QCD · Introduction · 0.81

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [10]

K. Iida, Phys. Rev. D 71, 054011(2005)

View on Pith 2005

[2] [11]

D. Blaschke and D. Sedrakian, nucl-th/0006038

View on Pith Pith review arXiv

[3] [1]

D. Bailin and A. Love, Phys. Rep. 107, 325 (1984); M. Iwasaki and T. Iwado, Phys. Lett. B 350, 163 (1995); M. Alford, K. Rajagopal, and F. Wilczek, Phys. Lett. B 422, 247 (1998); R. Rapp, T. Sch¨ afer, 12 E.V. Shuryak, and M. Velkovsky, Phys. Rev. Lett. 81, 53 (1998)

View on Pith 1984

[4] [2]

K. Iida, T. Matsuura, M. Tachibana and T. Hatsuda, Phys. R ev. Lett. 93, 132001 (2004); ibid Phys. Rev. D 71, 054003 (2005)

View on Pith 2004

[5] [3]

S.B. Ruster, I.A. Shovkovy, and D.H. Rischke, Nucl. Phys . A743, 127 (2004); K. Fukushima, C. Kou- varis, and K. Rajagopal, Phys. Rev. D 71, 034002(2005)

View on Pith 2004

[6] [4]

M. Alford, C. Kouvaris and K. Rajagopal, Phys. Rev. Lett. 92, 222001 (2004); Phys. Rev. D 71, 054009 (2005)

View on Pith 2004

[7] [5]

M. Huang and I. Shovkovy, Phys. Lett. B 564, 205 (2003); Nucl. Phys. A729, 835 (2003)

View on Pith 2003

[8] [6]

A. I. Larkin and Yu. N. Ovchinnikov, Sov. Phys. JETP 20, 762 (1965); P. Fulde and R. A. Ferrell, Phys. Rev. 135, A550 (1964)

View on Pith 1965

[9] [7]

M. G. Alford, J. A. Bowers and K. Rajagopal, Phys. Rev. D 63, 074016 (2001)

View on Pith 2001

[10] [8]

M. M. Forbes and A. R. Zhitnisky, Phys. Rev. D 65, 085009(2002)

View on Pith 2002

[11] [9]

K. Iida and G. Baym, Phys. Rev. D 66, 014015 (2002)

View on Pith 2002

[12] [12]

A. P. Balachandran, G. Marmo, N. Mukunda, J. S. Nilsson, E. C. G. Sudarshan, and F. Zaccaria, Phys. Rev. Lett 50, 1553 (1983); ibid Phys. Rev. D 29, 2919 (1984); ibid Phys. Rev. D 29, 2936 (1984); A. Abouelsaood, Phys. Lett. B 125, 467 (1983) and references therein

View on Pith 1983

[13] [13]

A. P. Balachandran and S. Digal, Int. J. Mod. Phys. A 17, 1149 (2002); A. P. Balachandran and S. Digal, Phys. Rev. D 66, 034018 (2002)

View on Pith 2002

[14] [14]

I. Giannakis and H. Ren, Nucl. Phys. B669, 462(2003)

View on Pith 2003

[15] [15]

I. Giannakis and H. Ren, Phys. Rev. D 65, 054017

View on Pith

[16] [16]

M. G. Alford, K. Rajagopal and F. Wilczek, Nucl. Phys. B537, 443(1999)

View on Pith 1999

[17] [17]

K. Iida and G. Baym, Phys. Rev. D 63, 074018 (2001); ibid. 66, 059903(E) (2002)

View on Pith 2001

[18] [18]

M. James, L. Perivolaropoulos, T. Vachaspati, Nucl. Ph ys. B395, 534(1993)

View on Pith 1993

[19] [19]

T. W. B. Kibble, J. Phys. A 9:1387-1398, (1976)

View on Pith 1976

[20] [20]

S. Rudaz, A. M. Srivastava and S. Verma, Int. J. Mod. Phys . A 14, 1591(1999)

View on Pith 1999

[21] [21]

M. Hindmarsch, A. Davis and R. H. Brandenberger, Phys. R ev. D 49, 1944 (1994)

View on Pith 1994

[22] [22]

S. Digal, A. M. Srivastava, Phys. Rev. Lett. 76:583-586,(1996); S. Digal, S. Sengupta, and A. M. Srivastava, Phys. Rev. D 58:103510,(1998)

View on Pith 1996

[23] [23]

M. G. Alford, J. Berges and K. Rajagopal, Nucl. Phys. B571, 269(2000)

View on Pith 2000