Inverse magnetic catalysis in QCD

Tamas G. Kovacs

Institute for Nuclear Research, Debrecen

with

Falk Bruckmann and Gergely Endrodi

Universitat Regensburg

July 31, 2013

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Is there always magnetic catalysis?

Common wisdom:chiral condensate increases with the magnetic field

Low energy effective models

First lattice study: D’Elia et al., 2010

But! Bali et al., 2012 : around Tc condensate can decrease

Physical quark masses

Continuum limit

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Dependence of the condensate on the magnetic field

Bali et al. PRD (2012)

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What happens if B is switched on?

Quark condensate:

〈ψψ〉(B)=1

Z

∫

dA e−S(A) det[D(A,B)+m]︸ ︷︷ ︸

“sea”

Tr[

(D(A,B)+m)−1]

︸ ︷︷ ︸

“valence”

Why does the condensate depend on B?

Spectrum of D(A,B) in given gauge backgound changes → “valence”

Typical gauge field A changes → “sea”

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Change of Dirac spectral density with BT = 142 MeV, Nt = 6, generated with B = 0

→ spectral density around zero increases with B

→ 〈ψψ〉 increases

→ magnetic catalysis

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How does B influence the gauge fields?

What happens to the gauge field if B is switched on?

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How does B influence the gauge fields?

What happens to the gauge field if B is switched on?

Polyakov loop increases (gets more ordered)

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Why does the Polyakov loop increase with B?

Quark action:

Sq =− logdet(D+m) =−∑ log(λi +m)

m small

→ fluctuations of Sq dominated by small eigenvalues

Quark action suppresses small Dirac eigenvalues

Few small eigenvalues ⇔ large Polyakov loop

T ≪ Tc → P ≈ 0 → many small modes (sχSB)

T ≫ Tc → P ≈ 1 → λ1 ∝ T (lowest Matsubara mode)

Quark action prefers large Polyakov loop;

switching on B enhances this effect

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Change in action versus the Polyakov loopScatter plot of 103 ×4 lattice configurations around Tc , generated with B = 0

∆Sq = logdet(D(0,A)+m)− logdet(D(B,A)+m)

85 90 95 100 1050.1

0.2

0.3

0.4

0.5

0.6

simple average (B=0)reweighted to B

∆Sq → exponentially suppressed by B

P

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The Polyakov loop and the condensate

Condensate:

ψψ ≈ ∑1

λi +m

m small → dominated by small eigenvalues

P large → fewer small eigenvalues

→ smaller condensate

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Polyakov loop versus quark condensateScatter plot of 103 ×4 lattice configurations around Tc

0.1 0.2 0.3 0.4 0.5 0.60

100

200

300

400

ψψ

P

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Competition between “sea” and “valence”

Magnetic field → more small Dirac eigenvalues

Valence

More small modes → larger condensate

Sea

suppresses configurations with many small modes

suppression enhanced by magnetic field

quark condensate decreases

“Sea” and “valence” compete

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Why does the “sea” win at Tc?

Tc cross-over — order parameter Polyakov loop

At Tc Polyakov loop effective potential flat

Small magnetic field contribution has large ordering effect

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Conclusions

Both catalysis and inverse catalysis

depend on small quark modes

Inverse catalysis:

suppression of small Dirac ev’s by B in the quark det

Contribution of B in det to the P-loop effective potential

becomes important at Tc

Small modes → sensitive to quark mass

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