arXiv subjects
Publications and source records attributed to Koenraad Schalm.
We study the holographic dual of a finite density system with both bosonic and fermionic degrees of freedom. There is no evidence for a universal bose-dominated ground state. Instead, depending on the relative conformal weights the preferred groundstate is either pure AdS-Reissner-Nordstrom, a holographic superconductor, an electron star, or a novel mixed state that is best characterized as a hairy electron star.
Conventional approaches to cosmology in supergravity assume the existence of multiple sectors that only communicate gravitationally. In principle these sectors decouple in the limit Planck mass to infinity. In practice such a limit is delicate: for generic supergravities, where sectors are combined by adding their Kahler functions, the separate superpotentials must contain non-vanishing vacuum expectation values supplementing the naive global superpotential. We show that this requires non-canonical scaling in the naive supergravity superpotential couplings to recover independent sectors of globally supersymmetric field theory in the decoupling limit Planck Mass to infinity.
We investigate the symmetry constraints on the bispectrum, i.e. the three-point correlation function of primordial density fluctuations, in slow-roll inflation. It follows from the defining property of slow-roll inflation that primordial correlation functions inherit most of their structure from weakly broken de Sitter symmetries. Using holographic techniques borrowed from the AdS/CFT correspondence, the symmetry constraints on the bispectrum can be mapped to a set of stress-tensor Ward identities in a weakly broken 2+1-dimensional Euclidean CFT. We construct the consistency condition from these Ward identities using conformal perturbation theory. This requires a second order Ward identity and the use of the evolution equation. Our result also illustrates a subtle difference between conformal perturbation theory and the slow roll expansion.
We compute the universal generic corrections to the power spectrum in slow-roll inflation due to unknown high-energy physics. We arrive at this result via a careful integrating out of massive fields in the "in-in" formalism yielding a consistent and predictive low-energy effective description in time-dependent backgrounds. The density power spectrum is universally modified at leading order in $H/M$, the ratio of the scale of inflation to the scale of new physics; the tensor power spectrum receives only subleading corrections. In doing so, we show how to make sense of a physical momentum-cut-off in loop integrals despite dynamical redshifts, and how the result can be captured in a combined effective action/effective density matrix, where the latter contains non-adiabatic terms which modify the boundary conditions.
We compute the model-independent contributions to the primordial bispectrum and trispectrum in de Sitter space due to high-energy physics. We do this by coupling a light inflaton to an auxiliary heavy field, and then evaluating correlation functions in the Schwinger-Keldysh "in-in" formalism. The high-energy physics produces corrections parametrized by $H/M$ where $H$ is the scale of inflation and $M$ is the mass of the heavy field. The bispectrum peaks near the elongated shape, but otherwise contains no features. The trispectrum receives no corrections at order $H/M$.
We study lattice effects in strongly coupled systems of fermions at a finite density described by a holographic dual consisting of fermions in Anti-de-Sitter space in the presence of a Reissner-Nordstrom black hole. The lattice effect is encoded by a periodic modulation of the chemical potential with a wavelength of order of the intrinsic length scales of the system. This corresponds with a highly complicated "band structure" problem in AdS, which we only manage to solve in the weak potential limit. The "domain wall" fermions in AdS encoding for the Fermi surfaces in the boundary field theory diffract as usually against the periodic lattice, giving rise to band gaps. However, the deep infrared of the field theory as encoded by the near horizon AdS2 geometry in the bulk reacts in a surprising way to the weak potential. The hybridization of the fermions bulk dualizes into a linear combination of CFT1 "local quantum critical" propagators in the bulk, characterized by momentum dependent exponents displaced by lattice Umklapp vectors. This has the consequence that the metals showing quasi-Fermi surfaces cannot be localized in band insulators. In the AdS2 metal regime, where the conformal dimension of the fermionic operator is large and no Fermi surfaces are present at low T/μ, the lattice gives rise to a characteristic dependence of the energy scaling as a function of momentum. We predict crossovers from a high energy standard momentum AdS2 scaling to a low energy regime where exponents found associated with momenta "backscattered" to a lower Brillioun zone in the extended zone scheme. We comment on how these findings can be used as a unique fingerprint for the detection of AdS2 like "pseudogap metals" in the laboratory.
We study holographic entanglement entropy in the background of charged dilatonic black holes which can be viewed as holographic duals of certain finite density states of N=4 super Yang-Mills. These charged black holes are distinguished in that they have vanishing ground state entropy. The entanglement entropy for a slab experiences a second order phase transition as the thickness of the slab is varied, while the entanglement entropy for a sphere is a smooth function of the radius. This suggests that the second scale introduced by the anisotropy of the slab plays an important role in driving the phase transition. In both cases we do not observe any logarithmic violation of the area law indicative of hidden Fermi surfaces. We investigate how these results are affected by the inclusion of the Gauss-Bonnet term in the bulk gravitational action. We also observe that such addition to the bulk action does not change the logarithmic violation of the area law in the backgrounds with hyperscaling violation.
We compute the universal generic corrections to the inflationary power spectrum due to unknown high-energy physics. We arrive at this result via a careful integrating out of massive fields in the "in-in" formalism yielding a consistent and predictive low-energy effective description in time-dependent backgrounds. We find that the power spectrum is universally modified at order H/M, where H is the scale of inflation. This is qualitatively different from the universal corrections in time-independent backgrounds, and it suggests that such effects may be present in upcoming cosmological observations.
We argue that the eta-problem in supergravity inflation cannot be solved without knowledge of the ground state of hidden sectors that are gravitationally coupled to the inflaton. If the hidden sector breaks supersymmetry independently, its fields cannot be stabilized during cosmological evolution of the inflaton. We show that both the subsequent dynamical mixing between sectors as well as the lightest mass of the hidden sector are set by the scale of supersymmetry breaking in the hidden sector. The true cosmological eta-parameter arises from a linear combination of the lightest mode of the hidden sector with the inflaton. Generically, either the true eta deviates considerably from the naïve eta implied by the inflaton sector alone, or one has to consider a multifield model. Only if the lightest mass in the hidden sector is much larger than the inflaton mass and if the inflaton mass is much larger than the scale of hidden sector supersymmetry breaking, is the effect of the hidden sector on the slow-roll dynamics of the inflaton negligible.
Despite intense efforts during the last 25 years, the physics of unconventional superconductors, including the cuprates with a very high transition temperature, is still a controversial subject. It is believed that superconductivity in many of these strongly correlated metallic systems originates in the physics of quantum phase transitions, but quite diverse perspectives have emerged on the fundamentals of the electron-pairing physics, ranging from Hertz style critical spin fluctuation glue to the holographic superconductivity of string theory. Here we demonstrate that the gross energy scaling differences that are behind these various pairing mechanisms are directly encoded in the frequency and temperature dependence of the dynamical pair susceptibility. This quantity can be measured directly via the second order Josephson effect and it should be possible employing modern experimental techniques to build a `pairing telescope' that gives a direct view on the origin of quantum critical superconductivity.
We provide new evidence that the holographic dual to a strongly coupled charged Fermi Liquid has a non-zero fermion density in the bulk. We show that the pole-strength of the stable quasiparticle characterizing the Fermi surface is encoded in the spatially averaged AdS probability density of a single normalizable fermion wavefunction in AdS. Recalling Migdal's theorem which relates the pole strength to the Fermi-Dirac characteristic discontinuity in the number density at $\ome_F$, we conclude that the AdS dual of a Fermi liquid is described by occupied on-shell fermionic modes in AdS. Encoding the occupied levels in the total probability density of the fermion field directly, we show that an AdS Reissner-Nordström black hole in a theory with charged fermions has a critical temperature, at which the system undergoes a first-order transition to a black hole with a non-vanishing profile for the bulk fermion field. Thermodynamics and spectral analysis confirm that the solution with non-zero AdS fermion-profile is the preferred ground state at low temperatures.
We argue that the electron star and the AdS Dirac hair solution are two limits of the free charged Fermi gas in AdS. Spectral functions of holographic duals to probe fermions in the background of electron stars have a free parameter that quantifies the number of constituent fermions that make up the charge and energy density characterizing the electron star solution. The strict electron star limit takes this number to be infinite. The Dirac hair solution is the limit where this number is unity. This is evident in the behavior of the distribution of holographically dual Fermi surfaces. As we decrease the number of constituents in a fixed electron star background the number of Fermi surfaces also decreases. An improved holographic Fermi groundstate should be a configuration that shares the qualitative properties of both limits.
Using AdS/CFT we investigate the effect of angular-momentum-induced anisotropy on the instantaneous drag force of a heavy quark. The dual description is that of a string moving in the background of a Kerr-AdS black holes. The system exhibits the expected focussing of jets towards the impact parameter plane. We put forward that we can use the connection between this focussing behavior and the angular momentum induced pressure gradient to extrapolate the pressure gradient correction to the drag force that can be used for transverse elliptic flow in realistic RHIC. The result is recognizable as a relativistic pressure gradient force.
We investigate the constraints of slow-roll inflation on the string worldsheet. A general gravity-matter set-up is used in which the worldsheet consists of an abstract CFT coupled to a 3+1 dimensional non-linear sigma model. The empirical slow-roll parameters are expressed in terms of the beta functions of operators in the matter/internal CFT and the beta function of the dilaton. The result confirms that inflation is only sensitive to macroscopic properties of the matter sector, and that in string theory inflation is a non-perturbative (in g_s) phenomenon and one must go beyond tree-level string theory.
A central problem in quantum condensed matter physics is the critical theory governing the zero temperature quantum phase transition between strongly renormalized Fermi-liquids as found in heavy fermion intermetallics and possibly high Tc superconductors. We present here results showing that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using the Anti-de-Sitter/Conformal Field Theory (AdS/CFT) correspondence to relate fermionic quantum critical fields to a gravitational problem, we compute the spectral functions of fermions in the field theory. By increasing the fermion density away from the relativistic quantum critical point, a state emerges with all the features of the Fermi-liquid.
Extremal charged black holes are BPS solutions. It is commonly thought that their nonextremal counterparts are not. Further, experience with BPS solutions in flat spacetime suggests that all BPS solutions are supersymmetric; i.e. that they are invariant under some supersymmetry charges of either the original field theory or an appropriately extended version thereof. Using nonextremal Reissner-Nordström black holes as counterexamples, we show that neither of these expectations is universally valid. These black holes correspond to a one-parameter family of BPS solutions. By showing that, subject to one very plausible assumption, no generalized Killing spinor can be constructed for these, we show that there is no supergravity theory for which these BPS solutions preserve a fraction of the supersymmetry, nor is there an associated Witten-Nester positive energy bound.
We study T^2 orientifolds and their moduli space in detail. Geometrical insight into the involutive automorphisms of T^2 allows a straightforward derivation of the moduli space of orientifolded T^2s. Using c=3 Gepner models, we compare the explicit worldsheet sigma model of an orientifolded T^2 compactification with the CFT results. In doing so, we derive half-supersymmetry preserving crosscap coefficients for generic unoriented Gepner models using simple current techniques to construct the charges and tensions of Calabi-Yau orientifold planes. For T^2s we are able to identify the O-plane charge directly as the number of fixed points of the involution; this number plays an important role throughout our analysis. At several points we make connections with the mathematical literature on real elliptic curves. We conclude with a preliminary extension of these results to elliptically fibered K3s.
We observe that the equation of motion for a free scalar field in a closed universe with radiation and a positive cosmological constant is given by Lamé's equation. Computing the exact power spectrum of scalar field perturbations, the presence of both curvature and radiation produces a red tilt weakly dependent on the amount of radiation.