14 research outputs found
On The S-Matrix of Ising Field Theory in Two Dimensions
We explore the analytic structure of the non-perturbative S-matrix in
arguably the simplest family of massive non-integrable quantum field theories:
the Ising field theory (IFT) in two dimensions, which may be viewed as the
Ising CFT deformed by its two relevant operators, or equivalently, the scaling
limit of the Ising model in a magnetic field. Our strategy is that of collider
physics: we employ Hamiltonian truncation method (TFFSA) to extract the
scattering phase of the lightest particles in the elastic regime, and combine
it with S-matrix bootstrap methods based on unitarity and analyticity
assumptions to determine the analytic continuation of the 2 to 2 S-matrix
element to the complex s-plane. Focusing primarily on the "high temperature"
regime in which the IFT interpolates between that of a weakly coupled massive
fermion and the E8 affine Toda theory, we will numerically determine 3-particle
amplitudes, follow the evolution of poles and certain resonances of the
S-matrix, and exclude the possibility of unknown wide resonances up to
reasonably high energies.Comment: typos corrected, references added, additional comparison with
perturbation theory added. 35 pages, 21 figure
Large Gauge Symmetries and Asymptotic States in QED
Large Gauge Transformations (LGT) are gauge transformations that do not
vanish at infinity. Instead, they asymptotically approach arbitrary functions
on the conformal sphere at infinity. Recently, it was argued that the LGT
should be treated as an infinite set of global symmetries which are
spontaneously broken by the vacuum. It was established that in QED, the Ward
identities of their induced symmetries are equivalent to the Soft Photon
Theorem. In this paper we study the implications of LGT on the S-matrix between
physical asymptotic states in massive QED. In appose to the naively free
scattering states, physical asymptotic states incorporate the long range
electric field between asymptotic charged particles and were already
constructed in 1970 by Kulish and Faddeev. We find that the LGT charge is
independent of the particles' momenta and may be associated to the vacuum. The
soft theorem's manifestation as a Ward identity turns out to be an outcome of
not working with the physical asymptotic states.Comment: 22 pages, 3 figures, v2: major revisio
No Particle Production in Two Dimensions: Recursion Relations and Multi-Regge Limit
We introduce high-energy limits which allow us to derive recursion relations
fixing the various couplings of Lagrangians of two-dimensional relativistic
quantum field theories with no tree-level particle production in a very
straightforward way. The sine-Gordon model, the Bullough-Dodd theory, Toda
theories of various kinds and the U(N) non-linear sigma model can all be
rediscovered in this way. The results here were the outcome of our explorations
at the 2017 Perimeter Institute Winter School.Comment: 20 page
Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
We study mesonic line operators in Chern-Simons theories with bosonic or
fermionic matter in the fundamental representation. In this paper, we elaborate
on the classification and properties of these operators using all loop
resummation of large perturbation theory. We show that these theories
possess two conformal line operators in the fundamental representation. One is
a stable renormalization group fixed point, while the other is unstable. They
satisfy first-order chiral evolution equations, in which a smooth variation of
the path is given by a factorized product of two mesonic line operators. The
boundary operators on which the lines can end are classified by their conformal
dimension and transverse spin, which we compute explicitly at finite 't Hooft
coupling. We match the operators in the bosonic and fermionic theories.Comment: 105 pages, 17 figures. v2: extended to mass deformed CS-matter
theories, (section 8). Some details about anomalous spin moved to appendix.
Typos corrected. JHEP versio
On the S-matrix of Ising field theory in two dimensions
Abstract
We explore the analytic structure of the non-perturbative S-matrix in arguably the simplest family of massive non-integrable quantum field theories: the Ising field theory (IFT) in two dimensions, which may be viewed as the Ising CFT deformed by its two relevant operators, or equivalently, the scaling limit of the Ising model in a magnetic field. Our strategy is that of collider physics: we employ Hamiltonian truncation method (TFFSA) to extract the scattering phase of the lightest particles in the elastic regime, and combine it with S-matrix bootstrap methods based on unitarity and analyticity assumptions to determine the analytic continuation of the 2 → 2 S-matrix element to the complex s-plane. Focusing primarily on the “high temperature” regime in which the IFT interpolates between that of a weakly coupled massive fermion and the E8 affine Toda theory, we will numerically determine 3-particle amplitudes, follow the evolution of poles and certain resonances of the S-matrix, and exclude the possibility of unknown wide resonances up to reasonably high energies
Exact quantization and analytic continuation
Abstract In this paper we give a streamlined derivation of the exact quantization condition (EQC) on the quantum periods of the Schrödinger problem in one dimension with a general polynomial potential, based on Wronskian relations. We further generalize the EQC to potentials with a regular singularity, describing spherical symmetric quantum mechanical systems in a given angular momentum sector. We show that the thermodynamic Bethe ansatz (TBA) equations that govern the quantum periods undergo nontrivial monodromies as the angular momentum is analytically continued between integer values in the complex plane. The TBA equations together with the EQC are checked numerically against Hamiltonian truncation at real angular momenta and couplings, and are used to explore the analytic continuation of the spectrum on the complex angular momentum plane in examples
Anyon Scattering from Lightcone Hamiltonian: the Singlet Channel
We study Chern-Simons theory coupled to massive fundamental fermions
in the lightcone Hamiltonian formalism. Focusing on the planar limit, we
introduce a consistent regularization scheme, identify the counter terms needed
to restore relativistic invariance, and formulate scattering theory in terms of
unambiguously defined asymptotic states. We determine the planar
S-matrix element in the singlet channel by solving the Lippmann-Schwinger
equation to all orders, establishing a result previously conjectured in the
literatureComment: 33 pages, 9 figure
Bootstrapping smooth conformal defects in Chern-Simons-matter theories
Abstract The expectation value of a smooth conformal line defect in a CFT is a conformal invariant functional of its path in space-time. For example, in large N holographic theories, these fundamental observables are dual to the open-string partition function in AdS. In this paper, we develop a bootstrap method for studying them and apply it to conformal line defects in Chern-Simons matter theories. In these cases, the line bootstrap is based on three minimal assumptions — conformal invariance of the line defect, large N factorization, and the spectrum of the two lowest-lying operators at the end of the line. On the basis of these assumptions, we solve the one-dimensional CFT on the line and systematically compute the defect expectation value in an expansion around the straight line. We find that the conformal symmetry of a straight defect is insufficient to fix the answer. Instead, imposing the conformal symmetry of the defect along an arbitrary curved line leads to a functional bootstrap constraint. The solution to this constraint is found to be unique
Line Operators in Chern-Simons-Matter Theories and Bosonization in Three Dimensions
We study Chern-Simons theories at large with either bosonic or fermionic
matter in the fundamental representation. The most fundamental operators in
these theories are mesonic line operators, the simplest example being Wilson
lines ending on fundamentals. We classify the conformal line operators along an
arbitrary smooth path as well as the spectrum of conformal dimensions and
transverse spins of their boundary operators at finite 't Hooft coupling. These
line operators are shown to satisfy first-order chiral evolution equations, in
which a smooth variation of the path is given by a factorized product of two
line operators. We argue that this equation together with the spectrum of
boundary operators are sufficient to uniquely determine the expectation values
of these operators. We demonstrate this by bootstrapping the two-point function
of the displacement operator on a straight line. We show that the line
operators in the theory of bosons and the theory of fermions satisfy the same
evolution equation and have the same spectrum of boundary operators.Comment: 12 pages, 3 figures. v2: typos corrected. v3: perturbative checks
added; minor improvement