String Gauge Symmetries in the Conformally Gauge-Fixed Polyakov D1 Brane Action in the Presence of Background Gauge Fields

Recently we have studied the instant-form quantization (IFQ) and the light-front quantization (LFQ) of the conformally gauge-fixed Polyakov D1 brane action using the Hamiltonian and path integral formulations. The IFQ is studied in the equal world-sheet time framework on the hyperplanes defined by the world- sheet time σ0 = τ = constant and the LFQ in the equal light-cone world-sheet time framework, on the hyperplanes of the light-front defined by the light-cone world-sheet time . The light-front theory is seen to be a constrained system in the sense of Dirac in contrast to the instant-form theory. However, owing to the gauge anomalous nature of these theories, both of these theories are seen to lack the usual string gauge symmetries defined by the world-sheet reparametrization invariance (WSRI) and the Weyl invariance (WI). In the present work we show that these theories when considered in the presence of background gauge fields such as the NSNS 2-form gauge field or in the presence of gauge field and the constant scalar axion field , then they are seen to possess the usual string gauge symmetries (WSRI and WI). In fact, these background gauge fields are seen to behave as the Wess-Zumino/Stueckelberg fields and the terms containing these fields are seen to behave as Wess-Zumino or Stueckelberg terms for these theories.

Light-Front Hamiltonian and Path Integral Formulations of the Conformally Gauge-Fixed Polyakov D1 Brane Action

In a recent paper we have studied the Hamiltonian and path integral quantizations of the conformally gauge-fixed Polyakov D1 brane action in the instant-form of dynamics using the equal world-sheet time framework on the hyperplanes defined by the world- sheet time . In the present work we quantize the same theory in the equal light-cone world-sheet time framework, on the hyperplanes of the light-front defined by the light-cone world-sheet time , using the standard constraint quantization techniques in the Hamiltonian and path integral formulations. The light-front theory is seen to be a constrained system in the sense of Dirac, which is in contrast to the corresponding case of the instant-form theory, where the theory remains unconstrained in the sense of Dirac. The light-front theory is seen to possess a set of twenty six primary second-class contraints. In the present work Hamiltonian and path integral quantizations of this theory are studied on the light-front.

Light-Front Hamiltonian and Path Integral Formulations of the Conformally Gauge-Fixed Polyakov D1 Brane Action with a Scalar Dilation Field

Recently we have studied the instant-form quantization (IFQ) of the conformally gauge-fixed Polyakov D1 brane action with and without a scalar dilaton field using the Hamiltonian and path integral formulations in the equal world-sheet time framework on the hyperplanes defined by the world- sheet time σ0=τ=constant . The light-front quantization (LFQ) of this theory without a scalar dilaton field has also been studied by us recently. In the present work we study the LFQ of this theory in the equal light-cone world-sheet time framework, on the hyperplanes of the light-front defined by the light-cone world-sheet time σ+=τ+σ=constant , using the Hamiltonian and path integral formulations. The light-front theory is seen to be a constrained system in the sense of Dirac. The light-front theory is seen to possess a set of twenty seven primary second-class contraints. In the present work Hamiltonian and path integral quantizations of this theory are studied on the light-front.

Instant-Form and Light-Front Hamiltonian and Path Integral Formulations of the Conformally Gauge-Fixed Polyakov D1-Brane Action in the Presence of a Scalar Axion Field and an <i>U</i>(1) Gauge Field

Recently we have studied the instant-form quantization (IFQ) and the light-front quantization (LFQ) of the conformally gauge-fixed Polyakov D1 brane action using the Hamiltonian and path integral formulations. The IFQ is studied in the equal world-sheet time framework on the hyperplanes defined by the world-sheet time σ0=τ=constant and the LFQ in the equal light-cone world-sheet time framework, on the hyperplanes of the light-front defined by the light-cone world-sheet time σ+= (τ+σ) =constant. The light-front theory is seen to be a constrained system in the sense of Dirac in contrast to the instant-form theory. However, owing to the gauge anomalous nature of these theories, both of these theories are seen to lack the usual string gauge symmetries defined by the world-sheet reparametrization invariance (WSRI) and the Weyl invariance (WI). In the present work we show that these theories when considered in the presence of background gauge fields such as the NSNS 2-form gauge field Bαβ(σ,τ) or in the presence of U(1) gauge field Aα(σ,τ) and the constant scalar axion field C(σ,τ), then they are seen to possess the usual string gauge symmetries (WSRI and WI). In fact, these background gauge fields are seen to behave as the Wess-Zumino or Stueckelberg fields and the terms containing these fields are seen to behave as Wess-Zumino or Stueckelberg terms for these theories.

D-brane superpotentials and Ooguri-Vafa invariants of compact Calabi-Yau threefolds

We calculate the D-brane superpotentials for two compact Calabi-Yau manifolds X14（1,1,2,3,7） and Xs （1,1,1,2,3） which are of non-Fermat type in the type II string theory. By constructing the open mirror symmetry, we also compute the Ooguri-Vafa invariants, which are related to the open Gromov-Witten invariants.

Dynamical brane creation and annihilation via a background flux

We study the dynamical Myers effect by allowing the fuzzy(or the dynamical dielectric brane)coordinates to be time dependent.We find three novel kinds of the dynamical spherical dielectric branes depending on their respective excess energies.The first represents a dynamical spherical brane carrying a negative excess energy(having a lower bound)with its radius oscillating periodically between two given non-zero values.The second is the one with zero excess energy and whose time dependence can be expressed in terms of a simple function.This particular dynamical spherical configuration represents the dielectric brane creation and/or annihilation like a photon in the presence of a background creating an electron-position pair and then annihilating back to a photon.The third is the one carrying positive excess energy and the radius can also oscillate periodically between two non-zero values but,unlike the first kind,it passes zero twice for each cycle.Each of the above can also be interpreted as the time evolution of a semi-spherical D-brane–anti semi-spherical D-brane system.

Beijing Lectures on the Grade Restriction Rule

The authors describe the relationships between categories of B-branes in dif- ferent phases of the non-Abelian gauged linear sigma model. The relationship is described explicitly for the model proposed by Hori and Tong with non-Abelian gauge group that connects two non-birational Calabi-Yau varieties studied by Rcdland. A grade restriction rule for this model is derived using the hemisphere partition function and it is used to map B-type D-branes between the two Calabi-Yau varieties.

Another representation of the β form of the inhomogeneous Picard-Fuchs equation

In this letter we give another representation of the β form in the inhomogeneous Picard-Fuchs equation for open topological string for some one-parameter Calabi-Yau hypersurfaces in weighted projective spaces. Furthermore, the corresponding domain wall tensions calculated by using these β forms are consistent with the results that appear in literature. The β form is essential for the calculation of the D-brane domain wall tension, and a convenient choice of β forms should simplify the calculation. The freedom of the choice of β forms shows some symmetries in Calabi-Yau space.

The dynamical creation/annihilation of a Dp-brane from D(p-2)branes

We discuss how to generate a dynamical Dp-brane with a topology of R^(p-2)×S^(2) from N D(p-2)-branes with R^(p-2) topology with or without the presence of a constant RR(p+2)-form flux.This extends the previous work(Chen and Lu 2004 arXiv:hep-th/0405265)of generating a dynamical spherical D2 brane from N DO branes in a constant RR four-form flux to a general p.In particular,dynamically generating a higher dimensional brane from lower dimensional ones does not necessarily need the presence of a relevant RR background flux but needs excess energy,lending support to the spacetime uncertainty principle.The time evolution of the dynamical p-brane for a general p remains the same as for the p=2 case,however there is a class of spatial dependent Dp configurations when p≥3.Some of these spatial-dependent Dp brane configurations and their properties have been discussed previously which can also be obtained from the time-dependent one by euclideanizing the time.Properties of the spatial-dependent solutions and their relations to the corresponding brane-anti brane system are discussed.