Lorentzian dynamics and factorization beyond rationality

We investigate the emergence of topological defect lines in the conformal Regge limit of two-dimensional conformal field theory. We explain how a local operator can be factorized into a holomorphic and an anti-holomorphic defect operator connected through a topological defect line, and discuss implications on analyticity and Lorentzian dynamics including aspects of chaos. We derive a formula relating the infinite boost limit, which holographically encodes the “opacity” of bulk scattering, to the action of topological defect lines on local operators. Leveraging the unitary bound on the opacity and the positivity of fusion coefficients, we show that the spectral radii of a large class of topological defect lines are given by their loop expectation values. Factorization also gives a formula relating the local and defect operator algebras and fusion categorical data. We then review factorization in rational conformal field theory from a defect perspective, and examine irrational theories. On the orbifold branch of the c = 1 free boson theory, we find a unified description for the topological defect lines through which the twist fields are factorized; at irrational points, the twist fields factorize through “non-compact” topological defect lines which exhibit continuous defect operator spectra. Along the way, we initiate the development of a formalism to characterize non-compact topological defect lines.

Constraining momentum space correlators using slightly broken higher spin symmetry

In this work, building up on [1] we present momentum space Ward identities related to broken higher spin symmetry as an alternate approach to computing correlators of spinning operators in interacting theories such as the quasi-fermionic and quasi-bosonic theories. The direct Feynman diagram approach to computing correlation functions is intricate and in general has been performed only in specific kinematic regimes. We use higher spin equations to obtain the parity even and parity odd contributions to two-, three- and four-point correlators involving spinning and scalar operators in a general kinematic regime, and match our results with existing results in the literature for cases where they are available.One of the interesting facts about higher spin equations is that one can use them away from the conformal fixed point. We illustrate this by considering mass deformed free boson theory and solving for two-point functions of spinning operators using higher spin equations.

Microscopic derivation of Ginzburg-Landau theories for hierarchical quantum Hall states

We propose a Ginzburg-Landau theory for a large and important part of the abelian quantum Hall hierarchy, including the prominently observed Jain sequences. By a generalized ``flux attachment" construction we extend the Ginzburg-Landau-Chern-Simons composite boson theory to states obtained by both quasielectron and quasihole condensation, and express the corresponding wave functions as correlators in conformal field theories. This yields a precise identification of the relativistic scalar fields entering these correlators in terms of the original electron field.

Advantages of the Mathematical Structure of a Dirac Fermion

The mathematical structure of quantum field theories of first order and of second order partial differential equations is analyzed. Relativistic properties of the Lagrangian density and the dimension of its elements are examined. The analysis is restricted to elementary massive particles that are elements of the Standard Model of particle physics. In the case of the first order Dirac equation, the dimensionless 4-vector γµ and the partial 4-derivative ∂µ whose dimension is [L−1],are elements of the mathematical structure of the theory. On the other hand, the mathematical structure of second order quantum equations has no dimensionless 4-vector which is analogous to γµ of the linear equation. It is proved that this deficiency is the root of inherent theoretical inconsistencies of second order quantum equations. Problems of the Klein-Gordon particle, the electroweak theory of the W±, Z particles and the Higgs boson theory are discussed.

Magnetic Monopoles in Multivector Boson Theories

A classical solution for a magnetic monopole is found in a specific multivector boson theory. We consider the model whose [SU(2)]N+1 gauge group is broken by sigma model fields (à la dimensional deconstruction) and further spontaneously broken by an adjoint scalar (à la triplet Higgs mechanism). In this multivector boson theory, we find the solution for the monopole whose mass is MN~(4πv/g)N+1, where g is the common gauge coupling constant and v is the vacuum expectation value of the triplet Higgs field, by using a variational method with the simplest set of test functions.