Inequalities for trace anomalies, length of the RG flow, distance between the fixed points and irreversibility

I discuss several issues about the irreversibility of the RG flow and the trace anomalies c, a and a'. First I argue that in quantum field theory: i) the scheme-invariant area Delta(a') of the graph of the effective beta function between the fixed points defines the length of the RG flow; ii) the minimum of Delta(a') in the space of flows connecting the same UV and IR fixed points defines the (oriented) distance between the fixed points; iii) in even dimensions, the distance between the fixed points is equal to Delta(a)=a_UV-a_IR. In even dimensions, these statements imply the inequalities 0 =< Delta(a)=< Delta(a') and therefore the irreversibility of the RG flow. Another consequence is the inequality a =< c for free scalars and fermions (but not vectors), which can be checked explicitly. Secondly, I elaborate a more general axiomatic set-up where irreversibility is defined as the statement that there exist no pairs of non-trivial flows connecting interchanged UV and IR fixed points. The axioms, based on the notions of length of the flow, oriented distance between the fixed points and certain "oriented-triangle inequalities", imply the irreversibility of the RG flow without a global a function. I conjecture that the RG flow is irreversible also in odd dimensions (without a global a function). In support of this, I check the axioms of irreversibility in a class of d=3 theories where the RG flow is integrable at each order of the large N expansion.Comment: 24 pages, 3 figures; expanded intro, improved presentation, references added - CQ

Holomorphic Currents and Duality in N=1 Supersymmetric Theories

Twisted supersymmetric theories on a product of two Riemann surfaces possess non-local holomorphic currents in a BRST cohomology. The holomorphic currents act as vector fields on the chiral ring. The OPE's of these currents are invariant under the renormalization group flow up to BRST-exact terms. In the context of electric-magnetic duality, the algebra generated by the holomorphic currents in the electric theory is isomorphic to the one on the magnetic side. For the currents corresponding to global symmetries this isomorphism follows from 't Hooft anomaly matching conditions. The isomorphism between OPE's of the currents corresponding to non-linear transformations of fields of matter imposes non-trivial conditions on the duality map of chiral ring. We consider in detail the $SU(N_c)$ SQCD with matter in fundamental and adjoint representations, and find agreement with the duality map proposed by Kutasov, Schwimmer and Seiberg.Comment: 19 pages, JHEP3 LaTex, typos correcte

HyperK\"ahler quotients and N=4 gauge theories in D=2

We consider certain N=4 supersymmetric gauge theories in D=2 coupled to quaternionic matter multiplets in a minimal way. These theories admit as effective theories sigma-models on non-trivial HyperK\"ahler manifolds obtained as HyperK\"ahler quotients. The example of ALE manifolds is discussed. (Based on a talk given by P. Fr\'e at the F. Gursey Memorial Conference, Istanbul, June 1994).Comment: 22 pages, Latex, no figure

The Linear Point: A cleaner cosmological standard ruler

We show how a characteristic length scale imprinted in the galaxy two-point correlation function, dubbed the "linear point", can serve as a comoving cosmological standard ruler. In contrast to the Baryon Acoustic Oscillation peak location, this scale is constant in redshift and is unaffected by non-linear effects to within $0.5$ percent precision. We measure the location of the linear point in the galaxy correlation function of the LOWZ and CMASS samples from the Twelfth Data Release (DR12) of the Baryon Oscillation Spectroscopic Survey (BOSS) collaboration. We combine our linear-point measurement with cosmic-microwave-background constraints from the Planck satellite to estimate the isotropic-volume distance $D_{V}(z)$, without relying on a model-template or reconstruction method. We find $D_V(0.32)=1264\pm 28$ Mpc and $D_V(0.57)=2056\pm 22$ Mpc respectively, consistent with the quoted values from the BOSS collaboration. This remarkable result suggests that all the distance information contained in the baryon acoustic oscillations can be conveniently compressed into the single length associated with the linear point.Comment: The optimal two-point correlation function bin-size is employed. Results are updated and the distance constraints are improve

On field theory quantization around instantons

With the perspective of looking for experimentally detectable physical applications of the so-called topological embedding, a procedure recently proposed by the author for quantizing a field theory around a non-discrete space of classical minima (instantons, for example), the physical implications are discussed in a ``theoretical'' framework, the ideas are collected in a simple logical scheme and the topological version of the Ginzburg-Landau theory of superconductivity is solved in the intermediate situation between type I and type II superconductors.Comment: 27 pages, 5 figures, LaTe

Structure of the Electric Flux in N=4 Supersymmetric Yang-Mills Theory

Correlators of Wilson loop operators with O_4=Tr(F_{\mu\nu}^2+...) are computed in N=4 super-Yang-Mills theory using the AdS/CFT correspondence. The results are compared with the leading order perturbative computations. As a consequence of conformal invariance, these correlators have identical forms in the weak and strong coupling limits for circular loops. They are essentially different for contours not protected by conformal symmetry.Comment: 7 pages, 1 postscript figure, minor corrections and clarifying argument

A three-loop check of the 'a - maximization' in SQCD with adjoint(s)

The 'a - maximization' was introduced by K. Inrtiligator and B. Wecht for finding anomalous dimensions of chiral superfields at the IR fixed points of the RG flow. Using known explicit calculations of anomalous dimensions in the perturbation theory of SQCD (with one or two additional adjoint fields), it is checked here at the three-loop level.Comment: 5 pages; the title changed, the text improved and expande

Tradeoff between extractable mechanical work, accessible entanglement, and ability to act as a reference system, under arbitrary superselection rules

Superselection rules (SSRs) limit the mechanical and quantum processing resources represented by quantum states. However SSRs can be violated using reference systems to break the underlying symmetry. We show that there is a duality between the ability of a system to do mechanical work and to act as a reference system. Further, for a bipartite system in a globally symmetric pure state, we find a triality between the system's ability to do local mechanical work, its ability to do ``logical work'' due to its accessible entanglement, and its ability to act as a shared reference system.Comment: 5 pages, no figures. Extended resubmitted version. Slightly modified title. Transferred to PR

Symmetry breaking and restoration for interacting scalar and gauge fields in Lifshitz type theories

We consider the one-loop effective potential at zero and finite temperature in field theories with anisotropic space-time scaling, with critical exponent $z=2$, including both scalar and gauge fields. Depending on the relative strength of the coupling constants for the gauge and scalar interactions, we find that there is a symmetry breaking term induced at one-loop at zero temperature and we find symmetry restoration through a first-order phase transition at high temperature.Comment: 12 pages, 2 figures, final version accepted in Phys. Let