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Browsing by Author "Jia, Bei"

Now showing 1 - 5 of 5
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    Aspects of Supersymmetry
    Jia, Bei (Virginia Tech, 2014-04-21)
    This thesis is devoted to a discussion of various aspects of supersymmetric quantum field theories in four and two dimensions. In four dimensions, 𝒩 = 1 supersymmetric quantum gauge theories on various four-manifolds are constructed. Many of their properties, some of which are distinct to the theories on flat spacetime, are analyzed. In two dimensions, general 𝒩 = (2, 2) nonlinear sigma models on S² are constructed, both for chiral multiplets and twisted chiral multiplets. The explicit curvature coupling terms and their effects are discussed. Finally, 𝒩 = (0, 2) gauged linear sigma models with nonabelian gauge groups are analyzed. In particular, various dualities between these nonabelian gauge theories are discussed in a geometric content, based on their Higgs branch structure.
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    Chiral operators in two-dimensional (0,2) theories and a test of triality
    Guo, Jirui; Jia, Bei; Sharpe, Eric R. (Springer, 2015-06-30)
    In this paper we compute spaces of chiral operators in general two-dimensional (0,2) nonlinear sigma models, both in theories twistable to the A/2 or B/2 model, as well as in non-twistable theories, and apply them to check recent duality conjectures. The fact that in a nonlinear sigma model, the Fock vacuum can act as a section of a line bundle on the target space plays a crucial role in our (0,2) computations, so we begin with a review of this property. We also take this opportunity to show how even in (2,2) theories, the Fock vacuum encodes in this way choices of target space spin structures, and discuss how such choices enter the A and B model topological field theories. We then compute chiral operators in general (0,2) nonlinear sigma models, and apply them to the recent Gadde-Gukov-Putrov triality proposal, which says that certain triples of (0,2) GLSMs should RG flow to nontrivial IR fixed points. We find that different UV theories in the same proposed universality class do not necessarily have the same space of chiral operators - but, the mismatched operators do not contribute to elliptic genera and are in non-integrable representations of the proposed IR affine symmetry groups, suggesting that the mismatched states become massive along RG flow. We find this state matching in examples not only of different geometric phases of the same GLSMs, but also in phases of different GLSMs, indirectly verifying the triality proposal, and giving a clean demonstration that (0,2) chiral rings are not topologically protected. We also check proposals for enhanced IR affine E-6 symmetries in one such model, verifying that (matching) chiral states in phases of corresponding GLSMs transform as 27's, (27) over bar.
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    D-branes and K-homology
    Jia, Bei (Virginia Tech, 2013-04-19)
    In this thesis the close relationship between the topological $K$-homology group of the spacetime manifold $X$ of string theory and D-branes in string theory is examined. An element of the $K$-homology group is given by an equivalence class of $K$-cycles $[M,E,\phi]$, where $M$ is a closed spin$^c$ manifold, $E$ is a complex vector bundle over $M$, and $\phi: M\rightarrow X$ is a continuous map. It is proposed that a $K$-cycle $[M,E,\phi]$ represents a D-brane configuration wrapping the subspace $\phi(M)$. As a consequence, the $K$-homology element defined by $[M,E,\phi]$ represents a class of D-brane configurations that have the same physical charge. Furthermore, the $K$-cycle representation of D-branes resembles the modern way of characterizing fundamental strings, in which the strings are represented as two-dimensional surfaces with maps into the spacetime manifold. This classification of D-branes also suggests the possibility of physically interpreting D-branes wrapping singular subspaces of spacetime, enlarging the known types of singularities that string theory can cope with.
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    Localization of twisted N=(0,2) gauged linear sigma models in two dimensions
    Closset, Cyril; Gu, Wei; Jia, Bei; Sharpe, Eric R. (Springer, 2016-03-14)
    We study two-dimensional N=(0, 2) supersymmetric gauged linear sigma models (GLSMs) using supersymmetric localization. We consider N=(0, 2) theories with an R-symmetry, which can always be defined on curved space by a pseudo-topological twist while preserving one of the two supercharges of flat space. For GLSMs which are deformations of N=(0, 2) GILSMs and retain a Coulomb branch, we consider the A/2-twist and compute the genus-zero correlation functions of certain pseudo-chiral operators, which generalize the simplest twisted chiral ring operators away from the N=(0, 2) locus. These correlation functions can be written in terms of a certain residue operation on the Coulomb branch, generalizing the Jeffrey-Kirwan residue prescription relevant for the N=(0, 2) locus. For abelian GLSMs, we reproduce existing results with new formulas that render the quantum sheaf cohomology relations and other properties manifest. For non-abelian GLSMs, our methods lead to new results. As an example, we briefly discuss the quantum sheaf cohomology of the C rassmannian manifold.
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    Notes on nonabelian (0,2) theories and dualities
    Jia, Bei; Sharpe, Eric R.; Wu, Ruoxu (Springer, 2014-08-05)
    In this paper we explore basic aspects of nonabelian (0,2) GLSMs in two dimensions for unitary gauge groups, an arena that until recently has largely been unexplored. We begin by discussing general aspects of (0,2) theories, including checks of dynamical supersymmetry breaking, spectators and weak coupling limits, and also build some toy models of (0,2) theories for bundles on Grassmannians, which gives us an opportunity to relate physical anomalies and trace conditions to mathematical properties. We apply these ideas to study (0,2) theories on Pfaffians, applying recent perturbative constructions of Pfaffians of Jockers et al.. We discuss how existing dualities in (2,2) nonabelian gauge theories have a simple mathematical understanding, and make predictions for additional dualities in (2,2) and (0,2) gauge theories. Finally, we outline how duality works in open strings in unitary gauge theories, and also describe why, in general terms, we expect analogous dualities in (0,2) theories to be comparatively rare.