53 research outputs found
Trace anomaly for non-relativistic fermions
We study the coupling of a 2+1 dimensional non-relativistic spin 1/2 fermion
to a curved Newton-Cartan geometry, using null reduction from an
extra-dimensional relativistic Dirac action in curved spacetime. We analyze
Weyl invariance in detail: we show that at the classical level it is preserved
in an arbitrary curved background, whereas at the quantum level it is broken by
anomalies. We compute the trace anomaly using the Heat Kernel method and we
show that the anomaly coefficients a, c are proportional to the relativistic
ones for a Dirac fermion in 3+1 dimensions. As for the previously studied
scalar case, these coefficents are proportional to 1/m, where m is the
non-relativistic mass of the particle.Comment: 23 page
On Newton-Cartan trace anomalies
We classify the trace anomaly for parity-invariant non-relativistic
Schr\"odinger theories in 2+1 dimensions coupled to background Newton-Cartan
gravity. The general anomaly structure looks very different from the one in the
z=2 Lifshitz theories. The type A content of the anomaly is remarkably
identical to that of the relativistic 3+1 dimensional case, suggesting the
conjecture that an a-theorem should exist also in the Newton-Cartan context.
Erratum: due to an overcounting of the number of linearly-independent terms
in the basis, the type A anomaly disappears if Frobenius condition is imposed.
See appended erratum for details. This crucial mistake was pointed out to us in
arXiv:1601.06795.Comment: 16 pages, V2:few equations corrected (final results unchanged),
references added, typos, V3: erratum include
Nonrelativistic trace and diffeomorphism anomalies in particle number background
Using the heat kernel method, we compute nonrelativistic trace anomalies for
Schr\"odinger theories in flat spacetime, with a generic background gauge field
for the particle number symmetry, both for a free scalar and a free fermion.
The result is genuinely nonrelativistic, and it has no counterpart in the
relativistic case. Contrary to the naive expectations, the anomaly is not
gauge-invariant; this is similar to the non-gauge covariance of the non-abelian
relativistic anomaly. We also show that, in the same background, the
gravitational anomaly for a nonrelativistic scalar vanishes.Comment: 20 pages; V2 minor changes also in title, typo
Renormalization properties of a Galilean Wess-Zumino model
We consider a Galilean N=2 supersymmetric theory in 2+1 dimensions with
F-term couplings, obtained by null reduction of a relativistic Wess-Zumino
model. We compute quantum corrections and we check that, as for the
relativistic parent theory, the F-term does not receive quantum corrections.
Even more, we find evidence that the causal structure of the non-relativistic
dynamics together with particle number conservation constrain the theory to be
one-loop exact.Comment: 41 pages, 21 figures; v2: references adde
Nonrelativistic near-BPS corners of super-Yang-Mills with symmetry
We consider limits of super Yang-Mills (SYM) theory that
approach BPS bounds and for which an structure is preserved. The
resulting near-BPS theories become non-relativistic, with a symmetry
emerging in the limit that implies the conservation of particle number. They
are obtained by reducing SYM on a three-sphere and subsequently
integrating out fields that become non-dynamical as the bounds are approached.
Upon quantization, and taking into account normal-ordering, they are consistent
with taking the appropriate limits of the dilatation operator directly, thereby
corresponding to Spin Matrix theories, found previously in the literature. In
the particular case of the near-BPS/Spin Matrix theory, we find a
superfield formulation that applies to the full interacting theory. Moreover,
for all the theories we find tantalizingly simple semi-local formulations as
theories living on a circle. Finally, we find positive-definite expressions for
the interactions in the classical limit for all the theories, which can be used
to explore their strong coupling limits. This paper will have a companion paper
in which we explore BPS bounds for which a structure is preserved.Comment: 62 pages, 2 figures; v2: minor correction
Volume and complexity for warped AdS black holes
We study the Complexity=Volume conjecture for Warped AdS black holes. We
compute the spatial volume of the Einstein-Rosen bridge and we find that its
growth rate is proportional to the Hawking temperature times the
Bekenstein-Hawking entropy. This is consistent with expectations about
computational complexity in the boundary theory.Comment: 18 pages, 3 figures, V2: refs adde
The Panorama of Spin Matrix Theory
Spin Matrix theory describes near-BPS limits of SYM theory,
which enables us to probe finite effects like D-branes and black hole
physics. In previous works, we have developed the spherical reduction and spin
chain methods to construct Spin Matrix theory for various limits. In this
paper, by considering a supercharge which is cubic in terms of
the letters, we construct the Hamiltonian of the largest Spin Matrix theory of
SYM, called the PSU Spin Matrix theory, as . We show the resulting Hamiltonian is
automatically positive definite and manifestly invariant under supersymmetry.
The Hamiltonian is made of basic blocks which transform as supermultiplets. A
novel feature of this Hamiltonian is its division into D-terms and F-terms that
are separately invariant under PSU symmetry and positive definite. As
all the other Spin Matrix theories arising from SYM can be
acquired by turning off certain letters in the theory, we consider our work as
revealing the "Panorama" of Spin Matrix theory.Comment: 32+11 pages, 3 figures; v2: minor changes; v3: journal version with
minor change
Shape Deformations of Charged R\'enyi Entropies from Holography
Charged and symmetry-resolved R\'enyi entropies are entanglement measures
quantifying the degree of entanglement within different charge sectors of a
theory with a conserved global charge. We use holography to determine the
dependence of charged R\'enyi entropies on small shape deformations away from a
spherical or planar entangling surface in general dimensions. This dependence
is completely characterized by a single coefficient appearing in the two point
function of the displacement operator associated with the R\'enyi defect. We
extract this coefficient using its relation to the one point function of the
stress tensor in the presence of a deformed entangling surface. This is mapped
to a holographic calculation in the background of a deformed charged black hole
with hyperbolic horizon. We obtain numerical solutions for different values of
the chemical potential and replica number in various spacetime dimensions,
as well as analytic expressions for small chemical potential near . When
the R\'enyi defect becomes supersymmetric, we demonstrate a conjectured
relation between the two point function of the displacement operator and the
conformal weight of the twist operator.Comment: 35+16 pages, 9 figure
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