Mostrando recursos 1 - 20 de 371

  1. Building blocks for generalized heterotic/F-theory duality

    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...

  2. T-duality for circle bundles via noncommutative geometry

    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...

  3. D-brane probes, branched double covers, and noncommutative resolutions

    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...

  4. The mirror symmetry of K3 surfaces with non-symplectic automorphisms of prime order

    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.

  5. A new approach to the $N$-particle problem in QM

    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...

  6. T-duality for Langlands dual groups

    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.

  7. Precanonical quantization and the Schrödinger wave functional revisited

    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...

  8. Topological field theory on a lattice, discrete theta-angles and confinement

    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...

  9. Geometric engineering of (framed) BPS states

    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...

  10. A unified quantum theory I: gravity interacting with a Yang-Mills field

    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.

  11. Standard modules, induction and the structure of the Temperley-Lieb algebra

    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...

  12. Topological strings, D-model, and knot contact homology

    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....

  13. The phase space for the Einstein-Yang-Mills equations and the first law of black hole thermodynamics

    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...

  14. A McKay-like correspondence for $(0,2)$-deformations

    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...

  15. Quantum phase transition of light in coupled optical cavity arrays: A renormalization group study

    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...

  16. Theory of intersecting loops on a torus

    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.

  17. Area inequalities for stable marginally outer trapped surfaces in Einstein-Maxwell-dilaton theory

    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...

  18. An exact expression for photon polarization in Kerr geometry

    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...

  19. The Sen limit

    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...

  20. Noncommutative connections on bimodules and Drinfeld twist deformation

    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...

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