arXiv subjects

H. Verschelde

Publications and source records attributed to H. Verschelde.

At least 19 recordsLinked to original sources

arXiv2014

Random Walks in Rindler Spacetime and String Theory at the Tip of the Cigar

In this paper, we discuss Rindler space string thermodynamics from a thermal scalar point of view as an explicit example of the results obtained in JHEP 1402 (2014) 127. We discuss the critical behavior of the string gas and interpret this as a random walk near the black hole horizon. Combining field theory arguments with the random walk path integral picture, we realize (at genus one) the picture put forward by Susskind of a long string surrounding black hole horizons. We find that thermodynamics is dominated by a long string living at string-scale distance from the horizon whose redshifted temperature is the Rindler or Hawking temperature. We provide further evidence of the recent proposal for string theory at the tip of the cigar by comparing with the flat space orbifold approach to Rindler thermodynamics. We discuss all types of closed strings (bosonic, type II and heterotic strings).

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arXiv2014

Near-Hagedorn Thermodynamics and Random Walks: a General Formalism in Curved Backgrounds

In this paper we discuss near-Hagedorn string thermodynamics starting from the explicit path integral derivation recently found by JHEP 0607 (2006) 031. Their result is extended and the validity is checked by comparing with some known exact results. We compare this approach with the first-quantized one-loop result from the low energy effective field theory and establish correction terms to the above result.

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arXiv2013

Holographic rho mesons in an external magnetic field

We study the rho meson in a uniform magnetic field eB using a holographic QCD-model, more specifically a D4/D8/Dbar8 brane setup in the confinement phase at zero temperature with two quenched flavours. The parameters of the model are fixed by matching to corresponding dual field theory parameters at zero magnetic field. We show that the up- and down-flavour branes respond differently to the presence of the magnetic field in the dual QCD-like theory, as expected because of the different electromagnetic charge carried by up- and down-quark. We discuss how to recover the Landau levels, indicating an instability of the QCD vacuum at eB = m_rho^2 towards a phase where charged rho mesons are condensed, as predicted by Chernodub using effective QCD-models. We improve on these existing effective QCD-model analyses by also taking into account the chiral magnetic catalysis effect, which tells us that the constituent quark masses rise with eB. This turns out to increase the value of the critical magnetic field for the onset of rho meson condensation to eB = 1.1 m_rho^2 = 0.67 GeV^2. We briefly discuss the influence of pions, which turn out to be irrelevant for the condensation in the approximation made.

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arXiv2012

Spontaneous electromagnetic superconductivity of vacuum induced by a strong magnetic field: QCD and electroweak theory

Both in electroweak theory and QCD, the vacuum in strong magnetic fields develops charged vector condensates once a critical value of the magnetic field is reached. Both ground states have a similar Abrikosov lattice structure and superconducting properties. It is the purpose of these proceedings to put the condensates and their superconducting properties side by side and obtain a global view on this type of condensates. Some peculiar aspects of the superfluidity and backreaction of the condensates are also discussed.

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arXiv2011

Electromagnetically superconducting phase of vacuum in strong magnetic field: structure of superconductor and superfluid vortex lattices in the ground state

Recently it was shown that vacuum in a background of strong enough magnetic field becomes an electromagnetic superconductor due to interplay between strong and electromagnetic forces. The superconducting ground state of the vacuum is associated with a spontaneous emergence of quark-antiquark condensates which carry quantum numbers of charged rho mesons. The rho-meson condensate is an inhomogeneous structure made of the so-called rho vortices, which are parallel to the magnetic field axis. The condensation of the charged rho mesons induces a (much weaker) superfluid-like condensate with quantum numbers of the neutral rho mesons. In this paper we show that the vortices in the superconducting condensate organize themselves in an equilateral triangular lattice similarly to an ordinary type-II superconductor. We show that each of these superconductor vortices is accompanied by three superfluid vortices and three superfluid antivortices made of the neutral rho meson condensate. The superconductor vortex overlaps with one of the superfluid vortices. The superposition of the superconducting and superfluid vortex lattices has a honeycomb pattern.

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arXiv2011

Effective scalar fields in Yang-Mills theories

Scalar fields play a crucial role in the Standard model. On the other hand, in the weak-coupling regime there is an unsolved problem of the quadratic divergence of scalar masses. Thus, it is natural to turn to composite, or effective scalar fields in the strong-coupling regime. Lattice simulations provide information on the "actually existing" scalar fields in Yang-Mills theories. On the continuum-theory side, dual models predict existence of various low-dimension vacuum defects, including probably scalar particles. We are looking for correspondence between the two frameworks, of lattice phenomenology and dual models, and discuss possible applications to the theory of the Yang-Mills plasma in the deconfining phase. It is not ruled out that the effective scalars play important role in the plasma dynamics.

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arXiv2011

Notes on relativistic superfluidity and gauge/string duality

We consider selected topics of relativistic superfluidity within gauge/string duality. Non-relativistically, the only conservation law relevant to the hydrodynamic approximation is the energy-momentum conservation. Relativistically, one has to introduce an extra conserved U(1) current and an extra three-dimensional scalar field which is condensed. Finding out a proper U(1) symmetry becomes a crucial point. We emphasize that in dual models there do arise extra U(1) symmetries associated with wrapping of the strings around (extra) compact directions in Euclidean space-time. Moreover, if the geometry associated with an extra compact dimension is cigar-like then the corresponding U(1) symmetry could well be spontaneously broken. The emerging Goldstone particle survives in the hydrodynamic limit. A specific point is that the chemical potential conjugated with the corresponding U(1) charge is vanishing. Within the standard approach the vanishing chemical potential implies no superfluidity. We argue that an exotic liquid, introduced recently in the literature, with vanishing energy density and non-vanishing pressure represents a viable description of the liquid associated with 3d Goldstone particles in Euclidean space-time. Since it lives on the stretched membrane, it describes energy-momentum transport in the deep infrared. We discuss briefly possible applications to the quark-gluon plasma.

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arXiv2010

Two-component quark-gluon plasma in stringy models

The two-component liquid model reproduces the basic properties of the quark-gluon plasma as observed in heavy-ion collisions. The key dynamic element of the model is the existence of a light scalar. We argue that existence of such a scalar is a generic feature of stringy models of quantum chromodynamics. The lattice data provide evidence for a condensed, three-dimensional scalar field as well. We outline a possible crucial check of the model on the lattice.

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arXiv2010

The asymmetry of the dimension 2 gluon condensate: the finite temperature case

In this paper, we continue the work begun in a previous article. We compute, in the formalism of local composite operators, the value of the asymmetry in the dimension two condensate for finite temperatures. We find a positive value for the asymmetry, which disappears when the temperature is increased. We also compute the value of the full dimension two condensate for higher temperatures, and we find that it decreases in absolute value, finally disappearing for sufficiently high temperature. We also comment on the temperature dependence of the electric and magnetic components of the condensate separately. We compare our results with the corresponding lattice date found by Chernodub and Ilgenfritz.

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arXiv2009

Aspects of the Gribov-Zwanziger framework

The existence of gauge (Gribov) copies disturbs the usual Faddeev-Popov quantization procedure in the Landau gauge. It is a very hard job to treat these in the continuum, even in a partial manner. A decent way to do so was worked out by Gribov, and later on by Zwanziger. The final point was a renormalizable action (the Gribov-Zwanziger action), implementing the restriction of the path integration to the so-called Gribov region, which is free of a subset of gauge copies, but not of all copies. Till recently, everybody agreed upon the fact that the restriction to the Gribov region implied a infrared enhanced ghost, and vanishing zero momentum gluon propagator. We discuss how the Gribov-Zwanziger action naturally leads to the existence of vacuum condensates of dimension two. As it is very common, such condensates can seriously alter the dynamics. In particular, the Gribov-Zwanziger condensates give rise to a gluon propagator with a finite but nonvanishing zero momentum limit, and reconstitute a nonenhanced ghost. We call this the refined Gribov-Zwanziger framework. The predictions are in qualitative agreement with most recent lattice simulations, and certain solutions of the Schwinger-Dyson equations. A crucial feature of the Gribov-Zwanziger framework is the soft (controllable) breaking of the BRST symmetry. We also point out that imposing the Kugo-Ojima confinement criterion on the Faddeev-Popov theory as a boundary condition from the beginning leads to the same partition function as of Gribov-Zwanziger, with associated BRST symmetry breaking. This clouds the interpretation of the Kugo-Ojima criterion in se.

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arXiv2009

A candidate for the scalar glueball operator within the Gribov-Zwanziger framework

This proceeding gives an overview of the renormalization of $F^2_{μν}$ using the Faddeev-Popov action and the more complicate Gribov-Zwanziger action, which deals with Gribov copies. We show that using the Faddeev-Popov action, $F^2_{μν}$ mixes with other $d=4$ operators. However, due to the BRST invariance of the action, this mixing is not relevant at the level of the correlator, $\Braket {F^2_{μν}(x) F^2_{αβ}(y)}$. In contrast, when turning to the Gribov-Zwanziger action, the mixing of $F^2_{μν}$ with other $d=4$ operator does have consequences at the level of the correlator. This is due to the breaking of the BRST. We then present a possible candidate for a physical operator in the Gribov-Zwanziger framework.

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arXiv2009

The asymmetry of the dimension 2 gluon condensate: the zero temperature case

We provide an algebraic study of the local composite operators A_μA_ν-δ_{μν}/d A^2 and A^2, with d=4 the spacetime dimension. We prove that these are separately renormalizable to all orders in the Landau gauge. This corresponds to a renormalizable decomposition of the operator A_μA_νinto its trace and traceless part. We present explicit results for the relevant renormalization group functions to three loop order, accompanied with various tests of these results. We then develop a formalism to determine the zero temperature effective potential for the corresponding condensates, and recover the already known result for \neq 0, together with =0, a nontrivial check that the approach is consistent with Lorentz symmetry. The formalism is such that it is readily generalizable to the finite temperature case, which shall allow a future analytical study of the electric-magnetic symmetry of the condensate, which received strong evidence from recent lattice simulations by Chernodub and Ilgenfritz, who related their results to 3 regions in the Yang-Mills phase diagram.

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arXiv2009

Gribov no-pole condition, Zwanziger horizon function, Kugo-Ojima confinement criterion, boundary conditions, BRST breaking and all that

We aim to offer a kind of unifying view on two popular topics in the studies of nonperturbative aspects of Yang-Mills theories in the Landau gauge: the so-called Gribov-Zwanziger approach and the Kugo-Ojima confinement criterion. Borrowing results from statistical thermodynamics, we show that imposing the Kugo-Ojima confinement criterion as a boundary condition leads to a modified yet renormalizable partition function. We verify that the resulting partition function is equivalent with the one obtained by Gribov and Zwanziger, which restricts the domain of integration in the path integral within the first Gribov horizon. The construction of an action implementing a boundary condition allows one to discuss the symmetries of the system in the presence of the boundary. In particular, the conventional BRST symmetry is softly broken.

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arXiv2009

Magnetic component of gluon plasma and its viscosity

We discuss the role of the magnetic degrees of freedom of the gluon plasma in its viscosity. The main assumption is that motions of the magnetic component and of the rest of the plasma can be considered as independent. The magnetic component in the deconfined phase is described by a three-dimensional (Euclidean) field theory. The parameters of the theory can be estimated phenomenologically, from the lattice data. It is not ruled out that the magnetic component is superfluid.

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arXiv2008

A gauge invariant infrared stabilization of 3D Yang-Mills gauge theories

We demonstrate that the inversion method can be a very useful tool in providing an infrared stabilization of 3D gauge theories, in combination with the mass operator $A^2$ in the Landau gauge. The numerical results will be unambiguous, since the corresponding theory is ultraviolet finite in dimensional regularization, making a renormalization scale or scheme obsolete. The proposed framework is argued to be gauge invariant, by showing that the nonlocal gauge invariant operator $A^2_{\min}$, which reduces to $A^2$ in the Landau gauge, could be treated in 3D, in the sense that it is power counting renormalizable in any gauge. As a corollary of our analysis, we are able to identify a whole set of powercounting renormalizable nonlocal operators of dimension two.

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arXiv2008

A purely algebraic construction of a gauge and renormalization group invariant scalar glueball operator

This paper presents a complete algebraic proof of the renormalizability of the gauge invariant $d=4$ operator $F_{μν}^2(x)$ to all orders of perturbation theory in pure Yang-Mills gauge theory, whereby working in the Landau gauge. This renormalization is far from being trivial as mixing occurs with other $d=4$ gauge variant operators, which we identify explicitly. We determine the mixing matrix $Z$ to all orders in perturbation theory by using only algebraic arguments and consequently we can uncover a renormalization group invariant by using the anomalous dimension matrix $Γ$ derived from $Z$. We also present a future plan for calculating the mass of the lightest scalar glueball with the help of the framework we have set up.

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arXiv2008

The Landau gauge gluon and ghost propagator in the refined Gribov-Zwanziger framework in 3 dimensions

In previous works, we have constructed a refined version of the Gribov-Zwanziger action in 4 dimensions, by taking into account a novel dynamical effect. In this paper, we explore the 3-dimensional case. Analogously as in 4 dimensions, we obtain a ghost propagator behaving like $1/p^2$ in the infrared, while the gluon propagator reaches a finite nonvanishing value at zero momentum. Simultaneously, a clear violation of positivity by the gluon propagator is also found. This behaviour of the propagators turns out be in agreement with the recent numerical simulations.

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arXiv2008

The effects of Gribov copies in 2D gauge theories

In previous works, we have shown that the Gribov-Zwanziger action, which implements the restriction of the domain of integration in the path integral to the Gribov region, generates extra dynamical effects which influence the infrared behaviour of the gluon and ghost propagator in SU(N) Yang-Mills gauge theories. The latter are in good agreement with the most recent lattice data obtained at large volumes, both in 4D and in 3D. More precisely, the gluon propagator is suppressed and does not vanish at zero momentum, while the ghost propagator keeps a 1/p^2 behaviour for p^2\approx0. Instead, in 2D, the lattice data revealed a vanishing zero momentum gluon propagator and an infrared enhanced ghost, in support of the usual Gribov-Zwanziger scenario. We will now show that the 2D version of the Gribov-Zwanziger action still gives results in qualitative agreement with these lattice data, as the peculiar infrared nature of 2D gauge theories precludes the analogue of the dynamical effect otherwise present in 4D and 3D. Simultaneously, we also observe that the Gribov-Zwanziger restriction serves as an infrared regulating mechanism.

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