arXiv subjects
Publications and source records attributed to Rajamani Narayanan.
The overlap formulation is applied to an anomaly free combination of chiral fermions coupled to U(1) gauge fields on a 2D torus. Evidence is presented that gauge averaging the overlap phases in these models produces correct continuum results.
We consider anomaly free combinations of chiral fermions coupled to $U(1)$ gauge fields on a 2D torus first in the continuum and then on the lattice in the overlap formulation. Both in the continuum and on the lattice, when the background consists of sufficiently large constant gauge potentials the action induced by the fermions varies significantly under certain singular gauge transformations. ``Ruling away'' such discontinuities cannot be justified in the continuum framework and does not naturally fit on the lattice. Complete gauge invariance in the continuum can be restored in some models by choosing special boundary conditions for the fermions. Evidence is presented that gauge averaging the overlap phases in these models produces correct continuum results.
An overlap method for regularizing Majorana--Weyl fermions interacting with gauge fields is presented. A mod(2) index is introduced in relation to the anomalous violation of a discrete global chiral symmetry. Most of the paper is restricted to 2 dimensions but generalizations to 2+8k dimensions should be straightforward.
Golterman and Shamir falsely claim that a waveguide model modified by adding many charged bosonic spinors, in the limit of an infinite number of matter fields, becomes identical to the overlap if in the target theory every fermion appears in four copies. Their modified model would give wrong results even in the vectorial four flavor massless Schwinger model, while a dynamical simulation of this model with the overlap works correctly. In this note we pinpoint the error in the derivation of Golterman and Shamir.
In the continuum, the single flavor massless Schwinger model has an exact global axial $U(1)$ symmetry in the sector of perturbative gauge fields. This symmetry is explicitly broken by gauge fields with nonzero topological charge inducing a nonzero expectation value for the bilinear $\barψψ$. We show that a lattice formulation of this model, using the overlap formalism to treat the massless fermions, explicitly exhibits this phenomenon. A Monte Carlo simulation of the complete system yields the correct value of the fermion condensate and shows unambiguously that it originates from the sector of topological charge equal to unity.
We compute the two loop coefficient in the relation between the lattice bare coupling and the running coupling defined through the Schroedinger functional for the case of pure SU(2) gauge theory. This result is needed as one computational component to relate the latter to the MSbar-coupling, and it allows us to implement O(a) improvement of the Schroedinger functional to two-loop order. In addition, the two-loop beta-function is verified in a perturbative computation on the lattice, and the behavior of an improved bare coupling is investigated beyond one loop.
It is shown that the lattice overlap correctly reproduces the chiral determinant on a two dimensional torus in the presence of nontrivial background Polyakov loop variables.
Path integration over Euclidean chiral fermions is replaced by the quantum mechanics of an auxiliary system of non--interacting fermions. Our construction avoids the no--go theorem and faithfully maintains all the known important features of chiral fermions, including the violation of some perturbative conservation laws by gauge field configurations of non--trivial topology.
I present the recent developments in a specific sub-field of chiral gauge theories on the lattice. This sub-field pertains to the use of infinitely many fermi fields to describe a single chiral field. In this approach, both anomalous and anomaly free theories can be discussed in equal footing. It produces the correct anomaly in the continuum limit. It has the potential to describe fermion number violating processes in the presence of a gauge field background with non-trivial topological charge on a finite lattice.
An expression for the lattice effective action induced by chiral fermions in any even dimensions in terms of an overlap of two states is shown to have promising properties in two dimensions: The correct abelian anomaly is reproduced and instantons are suppressed.
The effective action induced by chiral fermions can be written, formally, as an overlap of two states. These states are the Fock ground states of Hamiltonians for fermions in even dimensional space with opposite sign mass terms coupled to identical static vector potentials. A perturbative analysis of the overlap in the continuum framework produces the correct anomaly for Abelian gauge fields in two dimensions. When a lattice transfer matrix formalism is applied in the direction perpendicular to a domain wall on which chiral fermions live a lattice version of the overlap is obtained. The real part of the overlap is nonperturbatively defined and previous work indicates that the real part of the vacuum polarization tensor in four dimensions has the correct continuum limit for a chiral theory. The phase of the overlap represents the imaginary part of the chiral action and suffers from ambiguities.
We study the random walk representation of the two-point function in statistical mechanics models near the critical point. Using standard scaling arguments we show that the critical exponent $ν$ describing the vanishing of the physical mass at the critical point is equal to $ν_θ/ d_w$. $d_w$ is the Hausdorff dimension of the walk. $ν_θ$ is the exponent describing the vanishing of the energy per unit length of the walk at the critical point. For the case of O(N) models, we show that $ν_θ=φ$, where $φ$ is the crossover exponent known in the context of field theory. This implies that the Hausdorff dimension of the walk is $φ/ν$ for O(N) models.
We show that two recent independent proposals for regularizing a chiral gauge theory stem from one common trick. If the anomaly free complex representation carried by the right handed fermi--fields is $r$ one constructs a vector like theory with flavored right handed fermionic matter in $r+\bar r$ but with a mass matrix of the order of the cutoff and having an index equal to unity in an infinite dimensional flavor space. We present a Pauli--Villars realization of the trick that is likely to work to all orders in perturbation theory and a lattice version which is argued to produce the correct continuum leading order fermionic contribution to the vacuum polarization tensor and readied for further perturbative checks.
Schrödinger functional, the propagation kernel for going from some field configuration at time $x^0=0$ to some other configuration at $x^0=T$, is used to define a running coupling, $\bar g^2(L)$, at a length scale, $L$, in pure gauge theories. Using a lattice formulation and finite size scaling techniques, this running coupling is calculated non-perturbatively in the continuum for a wide range of $L$, that extends from the perturbative scales to non-perturbative scales, for the specific case of pure SU(2) gauge theory.
Following Symanzik we argue that the Schrödinger functional in lattice gauge theories without matter fields has a well-defined continuum limit. Due to gauge invariance no extra counter terms are required. The Schrödinger functional is, moreover, accessible to numerical simulations. It may hence be used to study the scaling properties of the theory and in particular the evolution of the renormalized gauge coupling from low to high energies. A concrete proposition along this line is made and the necessary perturbative analysis of the Schrödinger functional is carried through to 1-loop order.
The distance scale for a quantum field theory is the correlation length $ξ$, which diverges with exponent $ν$ as the bare mass approaches a critical value. If $t=m^{2}-m_{c}^{2}$, then $ξ=m_{P}^{-1} \sim t^{-ν}$ as $t \to 0$. The two-point function of a scalar field has a random walk representation. The walk takes place in a background of fluctuations (closed walks) of the field itself. We describe the connection between properties of the walk and of the two-point function. Using the known behavior of the two point function, we deduce that the dimension of the walk is $d_{w}=ϕ/ ν$ and that there is a singular relation between $t$ and the energy per unit length of the walk $θ\sim t^ϕ$ that is due to the singular behavior of the background at $t=0$. ($ϕ$ is a computable crossover exponent.)