Debye mass in de Sitter space

We calculate the one-loop contributions to the polarization operator for scalar quantum electrodynamics in different external electromagnetic and gravitational fields. In the case of gravity, de-Sitter space and its different patches were considered. It is shown that the Debye mass appears only in the case of alpha-vacuum in the Expanding Poincare Patch. It can be shown either by direct computations or by using analytical and casual properties of the de-Sitter space. Also, the case of constant electric field is considered and the Debye mass is calculated.Comment: 21 pages, 3 figure

Magic Angles In Equal-Twist Trilayer Graphene

We consider a configuration of three stacked graphene monolayers with equal consecutive twist angles $\theta$. Remarkably, in the chiral limit when interlayer coupling terms between $\textrm{AA}$ sites of the moir\'{e} pattern are neglected we find four perfectly flat bands (for each valley) at a sequence of magic angles which are exactly equal to the twisted bilayer graphene (TBG) magic angles divided by $\sqrt{2}$. Therefore, the first magic angle for equal-twist trilayer graphene (eTTG) in the chiral limit is $\theta_{*} \approx 1.05^{\circ}/\sqrt{2} \approx 0.74^{\circ}$. We prove this relation analytically and show that the Bloch states of the eTTG's flat bands are non-linearly related to those of TBG's. Additionally, we show that at the magic angles, the upper and lower bands must touch the four exactly flat bands at the Dirac point of the middle graphene layer. Finally, we explore the eTTG's spectrum away from the chiral limit through numerical analysis.Comment: 4 pages, 4 figures, 1 tabl

Non-Perturbative Defects in Tensor Models from Melonic Trees

The Klebanov-Tarnopolsky tensor model is a quantum field theory for rank-three tensor scalar fields with certain quartic potential. The theory possesses an unusual large $N$ limit known as the melonic limit that is strongly coupled yet solvable, producing at large distance a rare example of non-perturbative non-supersymmetric conformal field theory that admits analytic solutions. We study the dynamics of defects in the tensor model defined by localized magnetic field couplings on a $p$-dimensional subspace in the $d$-dimensional spacetime. While we work with general $p$ and $d$, the physically interesting cases include line defects in $d=2,3$ and surface defects in $d=3$. By identifying a novel large $N$ limit that generalizes the melonic limit in the presence of defects, we prove that the defect one-point function of the scalar field only receives contributions from a subset of the Feynman diagrams in the shape of melonic trees. These diagrams can be resummed using a closed Schwinger-Dyson equation which enables us to determine non-perturbatively this defect one-point function. At large distance, the solutions we find describe nontrivial conformal defects and we discuss their defect renormalization group (RG) flows. In particular, for line defects, we solve the exact RG flow between the trivial and the conformal lines in $d=4-\epsilon$. We also compute the exact line defect entropy and verify the $g$-theorem. Furthermore we analyze the defect two-point function of the scalar field and its decomposition via the operator-product-expansion, providing explicit formulae for one-point functions of bilinear operators and the stress-energy tensor.Comment: 47 pages, 10 figure

Beyond N=∞N=\infty in Large NN Conformal Vector Models at Finite Temperature

We investigate finite-temperature observables in three-dimensional large $N$ critical vector models taking into account the effects suppressed by $1\over N$. Such subleading contributions are captured by the fluctuations of the Hubbard-Stratonovich auxiliary field which need to be handled with care due to a subtle divergence structure which we clarify. The examples we consider include the scalar $O(N)$ model, the Gross-Neveu model, the Nambu-Jona-Lasinio model and the massless Chern-Simons Quantum Electrodynamics. We present explicit results for the free energy density to the subleading order, which also captures the one-point function of the stress-energy tensor, and include the dependence on a chemical potential. We further provide a formula from diagrammatics for the one-point functions of general single-trace higher-spin currents. We observe that in most cases considered, these subleading effects lift the apparent degeneracies between observables in different models at infinite $N$, while in special cases the discrepancies only start to appear at the next-to-subleading order.Comment: 67 pages, 9 figure

Deterministic Chaos in Integrable Models

In this work we present analytical and numerical evidences that classical integrable models possessing infinitely many degrees of freedom exhibit some features that are typical of chaotic systems. By studying how the conserved charges change under a small deformation of the initial conditions, we conclude that the inverse scattering map is responsible for this chaotic behavior, in spite of the system being integrable. We investigate this phenomenon in the explicit examples of the KdV equation and the sine-Gordon model and further provide general arguments supporting this statement.Comment: 19 pages, 4 figure