Karl Landsteiner

Instability of non-commutative SYM theories at finite temperature

We extend our previous work on the quasi-particle excitations in = 4 non-commutative U(1) Yang-Mills theory at finite temperature. We show that above some critical temperature there is a tachyon in the spectrum of excitations. It is a collective transverse photon mode polarized in the non-commutative plane. Thus the theory seems to undergo a phase transition at high temperature. Furthermore we find that the group velocity of quasi-particles generically exceeds the speed of light at low momentum.

Excitations in hot non-commutative theories

We study the dispersion relation for scalar excitations in supersymmetric, non-commutative theories at finite temperature. In = 4 Yang-Mills the low momentum modes have superluminous group velocity. In the massless Wess-Zumino model the minimum of the dispersion relation is at non zero momentum for temperatures above T0 ≈ (gθ)−1/2. We briefly comment on = 2 Yang-Mills at finite density.

Nonrelativistic noncommutative field theory and UV-IR mixing

We study a non-commutative non-relativistic scalar field theory in 211 dimensions. The theory shows the UV-IR mixing typical of QFT on non-commutative spaces. The one-loop correction to the two-point function turns out to be given by a d function in momentum space. The one-loop correction to the four-point function is of logarithmic type. We also evaluate the thermodynamic potential at two-loop order. To avoid an IR singularity we have to introduce a chemical potential. The suppression of the non-planar contribution with respect to the planar one turns out to depend crucially on the value of the chemical potential.

Moduli space ofN=2supersymmetricG2gauge theory

We apply the method of confining phase superpotentials to N = 2 supersymmetric Yang-Mills theory with the exceptional gauge group G_2. Our findings are consistent with the spectral curve of the periodic Toda lattice, but do not agree with the hyperelliptic curve suggested previously in the literature. We also apply the method to theories with fundamental matter, treating both the example of SO(5) and G_2.

The Thermodynamic potentials of Kerr - AdS black holes and their CFT duals

String or M-theory in the background of Kerr-AdS black holes is thought to be dual to the large N limit of certain conformal field theories on a rotating sphere at finite temperature. The five dimensional black hole is associated to = 4 supersymmetric Yang-Mills theory on a rotating three-sphere and the four dimensional one to the superconformal field theory of coinciding M2 branes on a rotating two-sphere. The thermodynamic potentials can be expanded in inverse powers of the radius of the sphere. We compute the leading and subleading terms of this expansion in the field theory at one loop and compare them to the corresponding supergravity expressions. The ratios between these terms at weak and strong coupling turn out not to depend on the rotation parameters in the case of = 4 SYM. For the field theory living on one M2 brane we find a subleading logarithmic term. No such term arises from the supergravity calculation.

Frequency dependence of the Chiral Vortical Effect

We study the frequency dependence of all the chiral vortical and magnetic conductivities for a relativistic gas of free chiral fermions and for a strongly coupled conformal field theory with holographic dual in four dimensions. Both systems have gauge and gravitational anomalies, and we compute their contribution to the conductivities. The chiral vortical conductivities and the chiral magnetic conductivity in the energy current show a frequency dependence in the form of a delta centered at zero frequency. This highly discontinuous behavior is a natural consequence of the Ward identities that include the energy momentum tensor. We discuss the physical interpretation of this result and its possible implications for the quark gluon plasma as created in heavy ion collisions. In the Appendix we discuss why the chiral magnetic effect seems to vanish in the consistent current for a particular implementation of the axial chemical potential.

Quasiparticles in Non-Commutative Field Theory

After a short introduction to the UV/IR mixing in non-commutative field theories we review the properties of scalar quasiparticles in non-commutative supersymmetric gauge theories at finite temperature. In particular we discuss the appearance of superluminous wave propagation.

The Zilch Vortical Effect.

We study the question of whether a helicity-transporting current is generated in a rotating photon gas at finite temperature. One problem is that there is no gauge-invariant local notion of helicity or helicity current. We circumvent this by studying not only the optical helicity current but also the gauge-invariant “zilch” current. In order to avoid problems of causality, we quantize the system on a cylinder of finite radius and then discuss the limit of infinite radius. We find that net helicity and zilch currents are only generated in the case of the finite radius and are due to duality-violating boundary conditions. A universal result exists for the current density on the axes of rotation in the high-temperature limit. To lowest order in the angular velocity, it takes a form similar to the well-known temperature dependence of the chiral vortical effect for chiral fermions. We briefly discuss possible relations to gravitational anomalies.