107 research outputs found

### Weyl and Ricci gauging from the coset construction

In this paper we demonstrate how, using the coset construction, a theory can
be systematically made Weyl invariant by gauging the scale symmetry. We show
that an analog of the inverse Higgs constraint allows the elimination of the
Weyl vector (gauge) field in favor of curvatures. We extend the procedure --
previously coined Ricci gauging -- and discuss its subtlety for the case of
theories with higher derivatives of conformally variant fields.Comment: 20 pages, no figures -- typos corrected, matches published versio

### Large-N Solution of the Heterotic Weighted Non-Linear Sigma-Model

We study a heterotic two-dimensional N=(0,2) gauged non-linear sigma-model
whose target space is a weighted complex projective space. We consider the case
with N positively and N^~=N_F - N negatively charged fields. This model is
believed to give a description of the low-energy physics of a non-Abelian
semi-local vortex in a four-dimensional N=2 supersymmetric U(N) gauge theory
with N_F > N matter hypermultiplets. The supersymmetry in the latter theory is
broken down to N=1 by a mass term for the adjoint fields. We solve the model in
the large-N approximation and explore a two-dimensional subset of the mass
parameter space for which a discrete Z_{N-N^~} symmetry is preserved.
Supersymmetry is generically broken, but it is preserved for special values of
the masses where a new branch opens up and the model becomes super-conformal.Comment: 34 pages, 10 figures, references adde

### General coordinate invariance in quantum many-body systems

We extend the notion of general coordinate invariance to many-body, not
necessarily relativistic, systems. As an application, we investigate
nonrelativistic general covariance in Galilei-invariant systems. The peculiar
transformation rules for the background metric and gauge fields, first
introduced by Son and Wingate in 2005 and refined in subsequent works, follow
naturally from our framework. Our approach makes it clear that Galilei or
Poincare symmetry is by no means a necessary prerequisite for making the theory
invariant under coordinate diffeomorphisms. General covariance merely expresses
the freedom to choose spacetime coordinates at will, whereas the true, physical
symmetries of the system can be separately implemented as "internal" symmetries
within the vielbein formalism. A systematic way to implement such symmetries is
provided by the coset construction. We illustrate this point by applying our
formalism to nonrelativistic s-wave superfluids.Comment: 14 pages; v2: minor update with additional references and
acknowledgments, version to appear in Phys. Rev.

### Monopole decay in the external electric field

The possibility of the magnetic monopole decay in the constant electric field
is investigated and the exponential factor in the probability is obtained.
Corrections due to Coulomb interaction are calculated. The relation between
masses of particles for the process to exist is obtained.Comment: 13 pages, 8 figure

### (Re-)Inventing the Relativistic Wheel: Gravity, Cosets, and Spinning Objects

Space-time symmetries are a crucial ingredient of any theoretical model in
physics. Unlike internal symmetries, which may or may not be gauged and/or
spontaneously broken, space-time symmetries do not admit any ambiguity: they
are gauged by gravity, and any conceivable physical system (other than the
vacuum) is bound to break at least some of them. Motivated by this observation,
we study how to couple gravity with the Goldstone fields that non-linearly
realize spontaneously broken space-time symmetries. This can be done in
complete generality by weakly gauging the Poincare symmetry group in the
context of the coset construction. To illustrate the power of this method, we
consider three kinds of physical systems coupled to gravity: superfluids,
relativistic membranes embedded in a higher dimensional space, and rotating
point-like objects. This last system is of particular importance as it can be
used to model spinning astrophysical objects like neutron stars and black
holes. Our approach provides a systematic and unambiguous parametrization of
the degrees of freedom of these systems.Comment: 30 page

### Spectral Flow in Instanton Computations and the \boldmath{\b} functions

We discuss various differences in the instanton-based calculations of the
$\beta$ functions in theories such as Yang-Mills and $\mathbb{CP}(N\!-\!1)$ on
one hand, and $\lambda\phi^4$ theory with Symanzik's sign-reversed prescription
for the coupling constant $\lambda$ on the other hand. Although the
aforementioned theories are asymptotically free, in the first two theories,
instantons are topological, whereas the Fubini-Lipatov instanton in the third
theory is topologically trivial. The spectral structure in the background of
the Fubini-Lipatov instanton can be continuously deformed into that in the flat
background, establishing a one-to-one correspondence between the two spectra.
However, when considering topologically nontrivial backgrounds for Yang-Mills
and $\mathbb{CP}(N\!-\!1)$ theories, the spectrum undergoes restructuring. In
these cases, a mismatch between the spectra around the instanton and the
trivial vacuum occurs.Comment: 22 page

### Identifying Large Charge Operators

The Large Charge sector of Conformal Field Theory (CFT) can generically be
described through a semiclassical expansion around a superfluid background. In
this work, focussing on $U(1)$ invariant Wilson-Fisher fixed points, we study
the spectrum of spinning large charge operators. For sufficiently low spin
these correspond to the phonon excitations of the superfluid state. We discuss
the organization of these states into conformal multiplets and the form of the
corresponding composite operators in the free field theory limit. The latter
entails a mapping, built order-by-order in the inverse charge $n^{-1}$, between
the Fock space of vacuum fluctuations and the Fock space of fluctuations around
the superfluid state. We discuss the limitations of the semiclassical method,
and find that the phonon description breaks down for spins of order $n^{1/2}$
while the computation of observables is valid up to spins of order $n$.
Finally, we apply the semiclassical method to compute some conformal 3-point
and 4-point functions, and analyze the conformal block decomposition of the
latter with our knowledge of the operator spectrum.Comment: 45 pages + appendices, 5 figure

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