Construction Of Effective Action Research Articles

The infrared structure of Nambu-Goldstone bosons

The construction of effective actions for Nambu-Goldstone bosons, and the nonlinear sigma model, usually requires a target coset space G/H. Recent progresses uncovered a new formulation using only IR data without reference to the broken group G in the UV, by imposing the Adler’s zero condition, which can be seen to originate from the superselection rule in the space of degenerate vacua. The IR construction imposes a nonlinear shift symmetry on the Lagrangian to enforce the correct single soft limit amid constraints of the unbroken group H. We present a systematic study on the consequence of the Adler’s zero condition in correlation functions of nonlinear sigma models, by deriving the conserved current and the Ward identity associated with the nonlinear shift symmetry, and demonstrate how the old-fashioned current algebra emerges. The Ward identity leads to a new representation of on-shell amplitudes, which amounts to bootstrapping the higher point amplitudes from lower point amplitudes and adding new vertices to satisfy the Adler’s condition. The IR perspective allows one to extract Feynman rules for the mysterious extended theory of biadjoint cubic scalars residing in the subleading single soft limit, which was first discovered using the Cachazo-He-Yuan representation of scattering amplitudes. In addition, we present the subleading triple soft theorem in the nonlinear sigma model and show that it is also controlled by on-shell amplitudes of the same extended theory as in the subleading single soft limit.

Schwinger-Keldysh formalism. Part II: thermal equivariant cohomology

Causally ordered correlation functions of local operators in near-thermal quantum systems computed using the Schwinger-Keldysh formalism obey a set of Ward identities. These can be understood rather simply as the consequence of a topological (BRST) algebra, called the universal Schwinger-Keldysh superalgebra, as explained in our compan-ion paper [1]. In the present paper we provide a mathematical discussion of this topological algebra. In particular, we argue that the structures can be understood in the language of extended equivariant cohomology. To keep the discussion self-contained, we provide a ba-sic review of the algebraic construction of equivariant cohomology and explain how it can be understood in familiar terms as a superspace gauge algebra. We demonstrate how the Schwinger-Keldysh construction can be succinctly encoded in terms a thermal equivariant cohomology algebra which naturally acts on the operator (super)-algebra of the quantum system. The main rationale behind this exploration is to extract symmetry statements which are robust under renormalization group flow and can hence be used to understand low-energy effective field theory of near-thermal physics. To illustrate the general prin-ciples, we focus on Langevin dynamics of a Brownian particle, rephrasing some known results in terms of thermal equivariant cohomology. As described elsewhere, the general framework enables construction of effective actions for dissipative hydrodynamics and could potentially illumine our understanding of black holes.

Superfield approach to the construction of effective action in quantum field theory with extended supersymmetry

We review the current state of research on the construction of effective actions in supersymmetric quantum field theory. Special attention is paid to gauge models with extended supersymmetry in the superfield approach. The advantages of formulation of such models in harmonic superspace for the calculation of effective action are emphasized. Manifestly supersymmetric and manifestly gauge-invariant methods for constructing the low-energy effective actions and deriving the corrections to them are considered and the possibilities to obtain the exact solutions are discussed. The calculations of one-loop effective actions in N = 2 supersymmetric Yang–Mills theory with hypermultiplets and in N = 4 supersymmetric Yang–Mills theory are analyzed in detail. The relationship between the effective action in supersymmetric quantum field theory and the low-energy limit in superstring theory is discussed.

Background field formalism and construction of effective action for N = 2, d = 3 supersymmetric gauge theories

We review the background field method for three-dimensional Yang-Mills and Chern-Simons models in N = 2 superspace. Superfield proper time (heat kernel) techniques are developed and exact expressions of heat kernels for constant backgrounds are presented. The background field method and heat kernel techniques are applied for evaluating the low-energy effective actions in N = 2 supersymmetric Yang-Mills and Chern-Simons models as well as in N = 4 and N = 8 SYM theories.

Construction of the effective action in nonanticommutative supersymmetric field theories

We develop a general gauge invariant construction of the one-loop effective action for supersymmetric gauge field theories formulated in N=1/2 superspace. Using manifestly covariant techniques (the background superfield method and proper-time representations) adopted to the N=1/2 superspace we show how to define unambiguously the effective action of a matter multiplet (in fundamental and adjoint representations) and the vector multiplet coupled to a background N=1/2 gauge superfield. As an application of this construction we exactly calculate the low-energy one-loop effective action of matter multiplet and SU(2) SYM theory on the Abelian background.

Construction of effective actions in superspace

A functional method of calculating superspace effective actions in supersymmetric theories is developed by use of superfield functional integrals and multipole-expansion techniques. The superspace effective actions for supersymmetric QED and the supersymmetric $\mathrm{C}{\mathrm{P}}^{n\ensuremath{-}1}$ model are constructed by this method without reference to component-field calculations.