BV quantization of a generic degenerate quadratic lagrangian

Generalizing the Yang-Mills gauge theory, we provide the BV quantization of a field model with a generic almost-regular quadratic Lagrangian by use of the fact that the configuration space of such a field model is split into the gauge-invariant and gauge-fixing parts.Comment: 8 page

Einstein Equations, Cosmological Constant and all that

We suggest an interpretation of Einstein Equations of General Relativity at large scales in which the Cosmological constant is exactly zero in the limit of zero spacetime variations of fundamental constants. We argue that in a quasiclassical Universe such variation should be tiny which leads to a tiny value for the Dark Energy. Next, we suggest that the are two sources of the Dark Energy. The first is the variation in Newton's constant $G_N$. It is a form of Dark Energy in that it has negative pressure, but it differs from the Cosmological Constant by a negative contribution to the energy. The second is the contribution of (causal) nonlocalities to the Dark Energy. This comes together with a particular view of Quantum Mechanics and the wavefunction collapse, in particular. The collapse is neither dynamical nor subjective.Comment: 33 pages, version 2. Clarifications adde

Relations between supersymmetric structures in UV and IR for N=4\mathcal{N}=4 bad theories

We investigate options for the structure of the infrared fixed points of $\mathcal{N}=4$ bad theories in three dimensions. Unitarity constraints allow a number of possibilities, not necessarily a product of an interacting $\mathcal{N}=4$ SCFT and free theories. For each option we provide relations between the UV and IR $R-$symmetry groups. For some of them we give examples. In particular, the $\mathcal{N}4$ SU(2) SYM with two fundamental hypermultiplets is an example of a bad theory which flows to an interacting irreducible SCFT in the IR. The question of whether all the options are realized remains open.Comment: 26 pages, v2: discussion of SU(2) SYM with two fundamental hypers added, references added, some minor corrections, v3: typos corrected, minor changes, version published in JHE

Bootstrapping the \cN=1 SCFT in three dimensions

We suggest a way to implement conformal bootstrap program for the case of the ${\cal N}=1$ SCFT in three dimensions using the previous analysis of the Ising model in \cite{CB}. We find approximate values for the conformal dimensions of several operators and the central charge $C_T$, the coefficient in the two-point function of the stress-tensor. Bootstrapping this particular (minimal) SCFT is of special interest as it was suggested in \cite{CM} that it may realize supersymmetry in 2+1 dimensions in experiment. The values are in a good agreement with the previous estimate in \cite{CM}.Comment: 6 page

Aharony duality and monopole operators in three dimensions

We test dualities between three dimensional N = 2 gauge theories proposed by Aharony in [1] by comparing superconformal indices of dual theories. We also extend the discussion of chiral rings matching to include monopole operators.Comment: 21 page

Examples of global symmetry enhancement by monopole operators

We consider examples of global symmetry enhancement by monopole operators in three dimensional {\cal N}=4 gauge theories. These examples include unitary overbalanced quivers, quivers with non-simply laced gauge groups and nonlinear quivers.Comment: 19 pages, 13 figure

Quantum Field Theory, Causal Structures and Weyl Transformations

We suggest that in the proper definition, Quantum Field Theories are quantum mechanical system which 'live' on the space of causal structures ${\cal C}$ of spacetime. That is, for any QFT a Hilbert space ${\cal H}$ on which local operators live is assigned not for each Lorentzian metric $g$, but for each causal structure ${\cal C}$. In practice one uses 'conformal frames' which all provide equivalent descriptions of the same QFT. To put it differently, Quantum Field Theories only know about causal structure of spacetime, and not its full Lorentzian metric. The Weyl group and the local RG flow naturally arise when one compares equivalent descriptions in different conformal frames. This is reduced to the usual RG flow of coupling constants when one only compares descriptions in conformal frames related by spacetime-independent Weyl rescalings. We point out that in this picture minimal coupling of a QFT to the metric is inconsistent and comment on the necessary violation of the equivalence principle in the presence of scalars.Comment: 12 pages, v.2. physical motivation section extended, some statements clarified, typos and minor errors fixe

A comment on the enhancement of global symmetries in superconformal SU(2) gauge theories in 5D

Recently, the superconformal index for a class of 5-dimensional superconformal quantum field theories with gauge group SU(2) and $N_f$ flavors was computed in Kim, Kim, and Lee (2012) to a few low orders in the chemical potential and enhancement of the global symmetry to $E_{N_f+1}$ was confirmed to this low order. In this note I provide an argument that the information contained in these few low order terms in the expansion of the index is sufficient to prove the enhancement of global symmetries in the theories. So, in particular the expression for the indices must display the enhancement to all orders in the chemical potential.Comment: 6 pages; second version, typos correcte

Comments on paper by B.Lesche (Phys. Rev. E {\bf 70}, 017102 (2004)) "Renyi entropies and observables"

It is shown that Lesche's conclusions on instability of the Renyi entropy are the same for the Tsallis entropy, as well. Moreover, they are unjustified for both entropies.Comment: 3 pages revtex

On evolution of the purity of two nonidentical two-level atoms interecting with one-mode coherent field

The resonant interaction of two nonidentical two-level atoms with one mode of the electromagnetic field has been considered. The pure-state evolution of the atomic states for field initially in the coherent state and atoms in the ground state has been investigated. It has been shown that for intermediate values of the relative differences of two coupling constants the atoms as well as the field are returned most closely to a pure state at the revival time. The possibility of the maximally entangled states at the beginning of the collapse time has been discussed.Comment: 4 pages, 1 figure