2092019
Topological Membrane Solitons and Loop Orders of Membrane Scatterings in M-theory
Two topological issues on membranes in M-theory are studied: (1) Soliton is an important subject in M-theory. Under the framework of obstruction theory with the help from framed links in S 3 , we give a complete enumeration of topological membrane solitons in a string-admissible target-space of the form a product of Minkowskian space-times, tori, and K3-surfaces. Patching of these solitons and their topological charges are also defined and discussed. (2) Loop order of membrane scatterings is the basis for a perturbative Mtheory. We explore this concept with emphases on its distinct features from pointlike and stringlike particles. For completeness, a light exposition on homologies of compact oriented 3-manifolds is given in the Appendix.
14577943
Lorentz Surfaces and Lorentzian CFT --- with an appendix on quantization of string phase space
The interest in string Hamiltonian system has recently been rekindled due to its application to target-space duality. In this article, we explore another direction it motivates. In Sec.\ 1, conformal symmetry and some algebraic structures of the system that are related to interacting strings are discussed. These lead one naturally to the study of Lorentz surfaces in Sec.\ 2. In contrast to the case of Riemann surfaces, we show in Sec.\ 3 that there are Lorentz surfaces that cannot be conformally deformed into Mandelstam diagrams. Lastly in Sec.\ 4, we discuss speculatively the prospect of Lorentzian conformal field theory. 
Additionally, to have a view of what quantum picture a string Hamiltonian system may lead to, we discuss independently in the Appendix a formal geometric quantization of the string phase space.
116949875
A Degeneration formula of Gromov-Witten invariants with respect to a curve class for degenerations from blow-ups
In two very detailed, technical, and fundamental works, Jun Li constructed a theory of Gromov-Witten invariants for a singular scheme of the gluing form Y1 ∪D Y2 that arises from a degeneration W/A 1 and a theory of relative Gromov-Witten invariants for a codimension-1 relative pair (Y,D). As a summit, he derived a degeneration formula that relates a finite summation of the usual Gromov-Witten invariants of a general smooth fiber Wt of W/A 1 to the Gromov-Witten invariants of the singular fiber W0 = Y1 ∪D Y2 via gluing the relative pairs (Y1,D) and (Y2,D). The finite sum mentioned above depends on a relative ample line bundle H on W/A 1 . His theory has already applications to string theory and mathematics alike. For other new applications of Jun Li’s theory, one needs a refined degeneration formula that depends
341730
Target-space duality between simple compact Lie groups and Lie algebras under the Hamiltonian formalism: I. Remnants of duality at the classical level
AbstractIt has been suggested that a possible classical remnant of the phenomenon of target-space duality (T-duality) would be the equivalence of the classical string Hamiltonian systems. Given a simple compact Lie groupG with a bi-invariant metric and a generating function Γ suggested in the physics literature, we follow the above line of thought and work out the canonical transformation Φ generated by Γ together with an Ad-invariant metric and a B-field on the associated Lie algebra
$$\mathfrak{g}$$
 ofG so thatG and
$$\mathfrak{g}$$
 form a string target-space dual pair at the classical level under the Hamiltonian formalism. In this article, some general features of this Hamiltonian setting are discussed. We study properties of the canonical transformation Φ including a careful analysis of its domain and image. The geometry of the T-dual structure on
$$\mathfrak{g}$$
 is lightly touched. We leave the task of tracing back the Hamiltonian formalism at the quantum level to the sequel of this paper.
40162216
Azumaya noncommutative geometry and D-branes: An Origin of the master nature of D-branes
In this lecture I review how a matrix/Azumaya-type noncommutative geometry arises for D-branes in string theory and how such a geometry serves as an origin of the master nature of D-branes; and then highlight an abundance conjecture on D0-brane resolutions of singularities that is extracted and purified from a work of Douglas and Moore in 1996. A conjectural relation of our setting with `D-geometry' in the sense of Douglas is also given. The lecture is based on a series of works on D-branes with Shing-Tung Yau, and in part with Si Li and Ruifang Song.
18184003
On the splitting type of an equivariant vector bundle over a toric manifold
From the work of Lian, Liu, and Yau on ”Mirror Principle”, in the explicit computation of the Euler data Q = { Q0, Q1, � � � } for an equivariant concavex bundle E over a toric manifold, there are two places the structure of the bundle comes into play: (1) the multiplicative characteric class Q0 of V one starts with, and (2) the splitting type of E. Equivariant bundles over a toric manifold has been classified by Kaneyama, using data related to the linearization of the toric action on the base toric manifold. In this article, we relate the splitting type of E to the classifying data of Kaneyama. From these relations, we compute the splitting type of a couple of nonsplittable equivariant vector bundles over toric manifolds that may be of interest to string theory and mirror symmetry. A code in Mathematica that carries out the computation of some of these examples is attached.
15158838
Top-color-assisted supersymmetry
It is known that the supersymmetric flavor changing neutral current problem can be avoided if the squarks take the following mass pattern: namely, the first two generations with the same chirality are degenerate with masses around the weak scale, while the third generation is very heavy. We realize this scenario through the supersymmetric extension of a top-color model with gauge-mediated supersymmetry breaking.
124850278
Decay Widths of Excited Heavy Mesons from Quantum Chromodynamics Sum Rules in the Infinite Mass Limit
The widths for pionic decays of the lowest two excited doublets (0(+), 1(+)) and (1(+), 2(+)) of heavy mesons are studied with quantum Chromodynamics sum rules in the heavy quark effective theory. The interpolating currents used allow us to distinguish the two 1(+) states without contamination in the infinite mass Limit. The soft pion approximation is not used in the calculations.
43722033
Topological susceptibility near T-c in SU(3) gauge theory
Abstract Topological charge susceptibility χ t for pure gauge SU(3) theory at finite temperature is studied using anisotropic lattices. The over-improved stout-link smoothing method is utilized to calculate the topological charge. Near the phase transition point we find a rapid declining behavior for χ t with values decreasing from ( 188 ( 1 )  MeV ) 4 to ( 67 ( 3 )  MeV ) 4 as the temperature increased from zero temperature to 1.9 T c which demonstrates the existence of topological excitations far above T c . The 4th order cumulant c 4 of topological charge, as well as the ratio c 4 / χ t is also investigated. Results of c 4 show step-like behavior near T c while the ratio at high temperature agrees with the value as predicted by the diluted instanton gas model.
17597441
EXCITED HEAVY BARYON MASSES FROM THE 1/Nc EXPANSION OF HQET
The mass spectra of the L=1 orbitally excited heavy baryons with light quarks in both the spin-flavor symmetric and the mixed representations are studied by the $1/N_c$ expansion method in the framework of the heavy quark effective theory. The mixing effect between the baryons in the two representations is also considered. The general pattern of the spectrum is predicted which will be verified by the experiments in the near future.
118837551
New experimental limit on the electric dipole moment of the electron in a paramagnetic insulator
We report results of an experimental search for the intrinsic Electric Dipole Moment (EDM) of the electron using a solid-state technique. The experiment employs a paramagnetic, insulating gadolinium gallium garnet (GGG) that has a large magnetic response at low temperatures. The presence of the eEDM would lead to a small but non-zero magnetization as the GGG sample is subject to a strong electric field. We search for the resulting Stark-induced magnetization with a sensitive magnetometer. Recent progress on the suppression of several sources of background allows the experiment to run free of spurious signals at the level of the statistical uncertainties. We report our first limit on the eEDM of ( 5.57 ± 7.98 ± 0.12)×10 25 e·cm with 5 days of data averaging. The search for the electric dipole moment (EDM) of elementary particles is motivated to test the discrete symmetries assumed in the Standard Model (SM) of particle physics. An account of the different transformation properties of the EDM (a polar vector) and the spin (a pseudo-vector), the fundamental physical laws governing particles must violate both time-reversal (T) and parity-inversion (P) symmetries for a fermion to acquire an EDM [1]. While the phenomena of P violation is firmly established in numerous experiments, T violation has only been observed directly in the neutral kaon system [2], with more searches in the B system underway [3]. Measurements of EDMs of elementary particles use different experimental techniques, often on low energy systems at Q ≃ 0, to probe the physics of T violation (with no flavor-changing) at energy scales higher than tens of TeV, and could provide information complementary to that from high-energy collider experiments on the nature of symmetry breaking. The physics of T violation is often linked, via the CPT theorem, to the violation of the combined Charge conjugate (C) and P symmetry. The only confirmed source of CP violation in the SM is the complex phase of the CKM matrix (that describes the quark mixing in charged-current weak interactions). With it, the electron EDM (eEDM) manifests through high-order loop couplings that involve flavor-changing quark interactions with the exchange of W ± weak bosons. The resulting size of eEDM predicted within the framework of SM is no larger than 10 −38 e·cm, which is well beyond the reach of current experimental techniques. The current experimental upper bound is established using thallium atomic beams with a sensitivity of 1.6×10 −27 e·cm [4]. New sources of CP violation introduced by theories beyond