812 research outputs found
From Classical To Quantum Gravity: Introduction to Loop Quantum Gravity
We present an introduction to the canonical quantization of gravity performed
in loop quantum gravity, based on lectures held at the 3rd quantum geometry and
quantum gravity school in Zakopane in 2011. A special feature of this
introduction is the inclusion of new proposals for coupling matter to gravity
that can be used to deparametrize the theory, thus making its dynamics more
tractable. The classical and quantum aspects of these new proposals are
explained alongside the standard quantization of vacuum general relativity in
loop quantum gravity.Comment: 56 pages. Contribution to the Proceedings of the 3rd Quantum Geometry
and Quantum Gravity School in Zakopane (2011). v2: Typos corrected, various
small changes in presentation, version as published in Po
Lattice supersymmetry, superfields and renormalization
We study Euclidean lattice formulations of non-gauge supersymmetric models
with up to four supercharges in various dimensions. We formulate the conditions
under which the interacting lattice theory can exactly preserve one or more
nilpotent anticommuting supersymmetries. We introduce a superfield formalism,
which allows the enumeration of all possible lattice supersymmetry invariants.
We use it to discuss the formulation of Q-exact lattice actions and their
renormalization in a general manner. In some examples, one exact supersymmetry
guarantees finiteness of the continuum limit of the lattice theory. As a
consequence, we show that the desired quantum continuum limit is obtained
without fine tuning for these models. Finally, we discuss the implications and
possible further applications of our results to the study of gauge and
non-gauge models.Comment: 44 pages, 1 figur
Experimental Simulation of Symmetry-Protected Higher-Order Exceptional Points with Single Photons
Exceptional points (EPs) of non-Hermitian (NH) systems have recently
attracted increasing attention due to their rich phenomenology and intriguing
applications. Compared to the predominantly studied second-order EPs,
higher-order EPs have been assumed to play a much less prominent role because
they generically require the tuning of more parameters. Here we experimentally
simulate two-dimensional topological NH band structures using single-photon
interferometry, and observe topologically stable third-order EPs obtained by
tuning only two real parameters in the presence of symmetry. In particular, we
explore how different symmetries stabilize qualitatively different third-order
EPs: the parity-time symmetry leads to a generic cube-root dispersion, while a
generalized chiral symmetry implies a square-root dispersion coexisting with a
flat band. Additionally, we simulate fourfold degeneracies, composed of the
non-defective twofold degeneracies and second-order EPs. Our work reveals the
abundant and conceptually richer higher-order EPs protected by symmetries and
offers a versatile platform for further research on topological NH systems.Comment: 15 pages, 9 figure
F-theory and AdS_3/CFT_2
We construct supersymmetric AdS_3 solutions in F-theory, that is Type IIB
supergravity with varying axio-dilaton, which are holographically dual to 2d
N=(0,4) superconformal field theories with small superconformal algebra. In
F-theory these arise from D3-branes wrapped on curves in the base of an
elliptically fibered Calabi-Yau threefold Y_3 and correspond to strings in the
6d N=(1,0) theory obtained from F-theory on Y_3. The non-trivial fibration over
the wrapped curves implies a varying coupling of the N=4 Super-Yang-Mills
theory on the D3-branes. We compute the holographic central charges and show
that these agree with the field theory and with the anomalies of self-dual
strings in 6d. We complement our analysis with a discussion of the dual
M-theory solutions and a comparison of the central charges.Comment: 83 pages, v2: references added, typos correcte
An interlacing property of the signless Laplacian of threshold graphs
We show that for threshold graphs, the eigenvalues of the signless Laplacian
matrix interlace with the degrees of the vertices. As an application, we show
that the signless Brouwer conjecture holds for threshold graphs, i.e., for
threshold graphs the sum of the k largest eigenvalues is bounded by the number
of edges plus k + 1 choose 2.Comment: 14 pages, 3 figure
A Quantum Monte Carlo algorithm for non-local corrections to the Dynamical Mean-Field Approximation
We present the algorithmic details of the dynamical cluster approximation
(DCA), with a quantum Monte Carlo (QMC) method used to solve the effective
cluster problem. The DCA is a fully-causal approach which systematically
restores non-local correlations to the dynamical mean field approximation
(DMFA) while preserving the lattice symmetries. The DCA becomes exact for an
infinite cluster size, while reducing to the DMFA for a cluster size of unity.
We present a generalization of the Hirsch-Fye QMC algorithm for the solution of
the embedded cluster problem. We use the two-dimensional Hubbard model to
illustrate the performance of the DCA technique. At half-filling, we show that
the DCA drives the spurious finite-temperature antiferromagnetic transition
found in the DMFA slowly towards zero temperature as the cluster size
increases, in conformity with the Mermin-Wagner theorem. Moreover, we find that
there is a finite temperature metal to insulator transition which persists into
the weak-coupling regime. This suggests that the magnetism of the model is
Heisenberg like for all non-zero interactions. Away from half-filling, we find
that the sign problem that arises in QMC simulations is significantly less
severe in the context of DCA. Hence, we were able to obtain good statistics for
small clusters. For these clusters, the DCA results show evidence of non-Fermi
liquid behavior and superconductivity near half-filling.Comment: 25 pages, 15 figure
F-theory and 2d (0,2) Theories
F-theory compactified on singular, elliptically fibered Calabi-Yau five-folds
gives rise to two-dimensional gauge theories preserving N=(0,2) supersymmetry.
In this paper we initiate the study of such compactifications and determine the
dictionary between the geometric data of the elliptic fibration and the 2d
gauge theory such as the matter content in terms of (0,2) superfields and their
supersymmetric couplings. We study this setup both from a gauge-theoretic point
of view, in terms of the partially twisted 7-brane theory, and provide a global
geometric description based on the structure of the elliptic fibration and its
singularities. Global consistency conditions are determined and checked against
the dual M-theory compactification to one dimension. This includes a discussion
of gauge anomalies, the structure of the Green-Schwarz terms and the
Chern-Simons couplings in the dual M-theory supersymmetric quantum mechanics.
Furthermore, by interpreting the resulting 2d (0,2) theories as heterotic
worldsheet theories, we propose a correspondence between the geometric data of
elliptically fibered Calabi-Yau five-folds and the target space of a heterotic
gauged linear sigma-model (GLSM). In particular the correspondence between the
Landau-Ginsburg and sigma-model phase of a 2d (0,2) GLSM is realized via
different T-branes or gluing data in F-theory.Comment: 124 pages, 5 figures, v2: ref added, v3: typos corrected, discussion
of interactions extended, v4: updated section 12, v5: typos corrected and
refs adde
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