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Advances in Theoretical and Mathematical Physics
Advances in Theoretical and Mathematical Physics
Heckman, Jonathan J.; Lin, Hai; Yau, Shing-Tung
In this note we propose a generalization of heterotic/F-theory duality. We introduce a set of non-compact building blocks which we glue together to reach compact examples of generalized duality pairs. The F-theory
building blocks consist of non-compact elliptically fibered Calabi-Yau fourfolds which also admit a $K3$ fibration. The compact elliptic model obtained by gluing need not have a globally defined $K3$ fibration. By
replacing the $K3$ fiber of each F-theory building block with a $T^2$, we reach building blocks in a heterotic dual vacuum which includes a position dependent dilaton and three-form flux. These building blocks
are glued together to reach a heterotic...
Mathai, Varghese; Rosenberg, Jonathan
Recently Baraglia showed how topological T-duality can be extended to apply not only to principal circle bundles, but also to non-principal circle bundles. We show that his results can also be recovered via two other methods:
the homotopy-theoretic approach of Bunke and Schick, and the noncommutative geometry approach which we previously used for principal torus bundles. This work has several interesting byproducts, including a study
of the $K$-theory of crossed products by $\tilde{O}(2) = \mathrm{Isom}(\mathbb{R})$, the universal cover of $O(2)$, and some interesting facts about equivariant $K$-theory for $\mathbb{Z}/ 2$. In the final section of this
paper, some of these results are extended...
Addington, Nicolas M.; Segal, Edward P.; Sharpe, Eric R.
This paper describes D-brane probes of theories arising in abelian gauged linear sigma models (GLSMs) describing branched double covers and noncommutative resolutions thereof, via nonperturbative effects rather
than as the critical locus of a superpotential. As these theories can be described as IR limits of Landau- Ginzburg models, technically this paper is an exercise in utilizing (sheafy) matrix factorizations. For Landau-Ginzburg
models which are believed to flow in the IR to smooth branched double covers, our D-brane probes recover the structure of the branched double cover (and flat nontrivial $B$ fields), verifying previous results.
In addition to smooth branched double covers, the same...
Comparin, Paola; Lyons, Christopher; Priddis, Nathan; Suggs, Rachel
We consider K3 surfaces that possess a non-symplectic automorphism of prime order $p>2$ and we present, for these surfaces, a correspondence between the mirror symmetry of Berglund-Hübsch-Chiodo-Ruan
and that for lattice polarized K3 surfaces presented by Dolgachev.
Schröter, Joachim
In this paper the old problem of determining the discrete spectrum of a multi-particle Hamiltonian is reconsidered. The aim is to bring a fermionic Hamiltonian for arbitrary numbers $N$ of particles by analytical means
into a shape such that modern numerical methods can successfully be applied. For this purpose the Cook-Schroeck Formalism is taken as starting point. This includes the use of the occupation number representation.
It is shown that the $N$-particle Hamiltonian is determined in a canonical way by a fictional 2-particle Hamiltonian. A special approximation of this 2-particle operator delivers an approximation of the $N$-particle
Hamiltonian, which is the orthogonal sum...
Daenzer, Calder; van Erp, Erik
This article addresses the question of whether Langlands duality for complex reductive Lie groups may be implemented by T-dualization. We prove that for reductive groups whose simple factors are of Dynkin
type A, D, or E, the answer is yes.
Kanatchikov, Igor V.
We address the issue of the relation between the canonical functional Schrödinger representation in quantum field theory and the approach of precanonical field quantization proposed by the author, which requires
neither a distinguished time variable nor infinite-dimensional spaces of field configurations. We argue that the standard functional derivative Schrödinger equation can be derived from the precanonical Dirac-like
covariant generalization of the Schrödinger equation under the formal limiting transition $\gamma^0 \varkappa \to \delta(0)$, where the constant $\varkappa$ naturally appears within precanonical quantization as
the inverse of a small “elementary volume” of space. We obtain a formal explicit expression of the Schrödinger wave functional as...
Kapustin, Anton; Thorngren, Ryan
We study a topological field theory describing confining phases of gauge theories in four dimensions. It can be formulated on a lattice using a discrete 2-form field talking values in a finite abelian group
(the magnetic gauge group). We show that possible theta-angles in such a theory are quantized and labeled by quadratic functions on the magnetic gauge group. When the theta-angles vanish, the theory
is dual to an ordinary topological gauge theory, but in general it is not isomorphic to it. We also explain how to couple a lattice Yang-Mills theory to a TQFT of this kind so that the ’t...
Chuang, Wu-yen; Diaconescu, Duiliu-Emanuel; Manschot, Jan; Moore, Gregory W.; Soibelman, Yan
BPS quivers for $\mathcal{N} = 2 \: SU(N)$ gauge theories are derived via geometric engineering from derived categories of toric Calabi-Yau threefolds. While the outcome is in agreement of previous
low energy constructions, the geometric approach leads to several new results. An absence of walls conjecture is formulated for all values of $N$, relating the field theory BPS spectrum to large radius D-brane
bound states. Supporting evidence is presented as explicit computations of BPS degeneracies in some examples. These computations also prove the existence of BPS states of arbitrarily high spin and infinitely
many marginal stability walls at weak coupling. Moreover, framed quiver...
Gerhardt, Claus
Using the results and techniques of a previous paper where we proved the quantization of gravity we extend the former result by adding a Yang-Mills functional and a Higgs term to the Einstein-Hilbert action.
Ridout, David; Saint-Aubin, Yvan
The basic properties of the Temperley-Lieb algebra $\mathsf{TL}_n$ with parameter $\beta = q + q^{-1} , q \in \mathbb{C} \backslash \{ 0 \}$, are reviewed in a pedagogical way. The link and standard
(cell) modules that appear in numerous physical applications are defined and a natural bilinear form on the standard modules is used to characterise their maximal submodules. When this bilinear form has a
non-trivial radical, some of the standard modules are reducible and $\mathsf{TL}_n$ is non-semisimple. This happens only when $q$ is a root of unity. Use of restriction and induction allows for a finer description
of the structure of the...
Aganagic, Mina; Ekholm, Tobias; Ng, Lenhard; Vafa, Cumrun
We study the connection between topological strings and contact homology recently proposed in the context of knot invariants. In particular, we establish the proposed relation between the Gromov-Witten disk amplitudes
of a Lagrangian associated to a knot and augmentations of its contact homology algebra. This also implies the equality between the $Q$-deformed $A$-polynomial and the augmentation polynomial of knot contact
homology (in the irreducible case). We also generalize this relation to the case of links and to higher rank representations for knots. The generalization involves a study of the quantum moduli space of special Lagrangian
branes with higher Betti numbers probing the Calabi-Yau....
McCormick, Stephen
We use the techniques of Bartnik to show that the space of solutions to the Einstein-Yang-Mills constraint equations on an asymptotically flat manifold with one end and zero boundary components, has a Hilbert manifold
structure; the Einstein-Maxwell system can be considered as a special case. This is equivalent to the property of linearisation stability, which was studied in depth throughout the 70s [1, 2, 9, 11, 13, 18, 19].
¶ This framework allows us to prove a conjecture of Sudarsky and Wald, namely that the validity of the first law of black hole thermodynamics is a suitable condition for stationarity. Since we...
Aspinwall, Paul S.
We present a local computation of deformations of the tangent bundle for a resolved orbifold singularity $\mathbb{C}^d/G$. These correspond to $(0, 2)$-deformations of $(2, 2)$-theories. A McKay-like correspondence
is found predicting the dimension of the space of first-order deformations from simple calculations involving the group. This is confirmed in two dimensions using the Kronheimer-Nakajima quiver construction. In higher
dimensions such a computation is subject to nontrivial worldsheet instanton corrections and some examples are given where this happens. However, we conjecture that the special crepant resolution given by the
$G$-Hilbert scheme is never subject to such corrections, and show this is true in an...
Sarkar, Sujit
We study the quantum phase transition of light of a system when atom trapped in microcavities and interacting through the exchange of virtual photons. We predict the quantum phase transition between the photonic Coulomb
blocked induce insulating phase and anisotropic exchange induced photonic superfluid phase in the system due to the existence of two Rabi frequency oscillations. The renormalization group equation shows explicitly
that for this system there is no self-duality. The system also shows two Berezinskii-Kosterlitz-Thouless (BKT) transitions for the different physical situation of the system. The presence of single Rabi frequency oscillation
in the system leads to the BKT transition where...
Nelson, J. E.; Picken, R. F.
We continue our investigation into intersections of closed paths on a torus, to further our understanding of the commutator algebra of Wilson loop observables in $2+1$ quantum gravity, when the cosmological constant is
negative.We give a concise review of previous results, e.g. that signed area phases relate observables assigned to homotopic loops, and present new developments in this theory of intersecting loops on a torus. We
state precise rules to be applied at intersections of both straight and crooked/rerouted paths in the covering space $\mathbb{R}^2$. Two concrete examples of combinations of different rules are presented.
Fajman, David; Simon, Walter
We prove area inequalities for stable marginally outer trapped surfaces in Einstein-Maxwell-dilaton theory. Our inspiration comes on the one hand from a corresponding upper bound for the area in terms of the charges obtained
recently by Dain, Jaramillo and Reiris in the pure Einstein-Maxwell case without symmetries, and on the other hand from Yazadjiev's inequality in the axially symmetric Einstein-Maxwell-dilaton case. The common issue in
these proofs and in the present one is a functional $\mathcal{W}$ of the matter fields for which the stability condition readily yields an upper bound. On the other hand, the step which crucially depends on whether
or not...
Farooqui, Anusar; Kamran, Niky; Panangaden, Prakash
We analyze the transformation of the polarization of a photon
propagating along an arbitrary null geodesic in Kerr geometry.
The motivation comes from the problem of an observer trying to
communicate quantum information to another observer in Kerr
spacetime by transmitting polarized photons. It is essential that
the observers understand the relationship between their frames of
reference and also know how the photon’s polarization transforms
as it travels through Kerr spacetime. Existing methods to calculate
the rotation of the photon polarization (Faraday rotation) depend
on choices of coordinate systems, are algebraically complex and
yield results only in the weak-field limit.
¶ We give a closed-form expression for a parallel propagated frame
along...
Clingher, Adrian; Donagi, Ron; Wijnholt, Martijn
$F$-theory compactifications on elliptic Calabi-Yau manifolds may be related to IIb compactifications by taking a certain limit in complex structure moduli space, introduced by A. Sen. The limit has been characterized on the
basis of $SL(2, \mathrm{Z})$ monodromies of the elliptic fibration. Instead, we introduce a stable version of the Sen limit. In this picture the elliptic Calabi-Yau splits into two pieces, a $\mathbf{P}^1$-bundle and a conic
bundle, and the intersection yields the IIb space-time.We get a precise match between $F$-theory and perturbative type IIb. The correspondence is holographic, in the sense that physical quantities seemingly spread
in the bulk of the $F$-theory...
Aschieri, Paolo; Schenkel, Alexander
Given a Hopf algebra $H$, we study modules and bimodules over an algebra $A$ that carry an $H$-action, as well as their morphisms and connections. Bimodules naturally arise when considering noncommutative
analogues of tensor bundles. For quasitriangular Hopf algebras and bimodules with an extra quasi-commutativity property we induce connections on the tensor product over $A$ of two bimodules from connections
on the individual bimodules. This construction applies to arbitrary connections, i.e. not necessarily Hequivariant ones, and further extends to the tensor algebra generated by a bimodule and its dual. Examples of these
noncommutative structures arise in deformation quantization via Drinfeld twists of the...