On the symmetries of BF models and their relation with gravity

The perturbative finiteness of various topological models (e.g. BF models) has its origin in an extra symmetry of the gauge-fixed action, the so-called vector supersymmetry. Since an invariance of this type also exists for gravity and since gravity is closely related to certain BF models, vector supersymmetry should also be useful for tackling various aspects of quantum gravity. With this motivation and goal in mind, we first extend vector supersymmetry of BF models to generic manifolds by incorporating it into the BRST symmetry within the Batalin-Vilkovisky framework. Thereafter, we address the relationship between gravity and BF models, in particular for three-dimensional space-time.Comment: 29 page

New BPS Solitons in 2+1 Dimensional Noncommutative CP^1 Model

Investigating the solitons in the non-commutative $CP^{1}$ model, we have found a new set of BPS solitons which does not have counterparts in the commutative model.Comment: 8 pages, LaTeX2e, references added, improvements to discussions, Version to be published in JHE

Lost equivalence of nonlinear sigma and CP1CP^{1} models on noncommutative space

We show that the equivalence of nonlinear sigma and $CP^{1}$ models which is valid on the commutative space is broken on the noncommutative space. This conclusion is arrived at through investigation of new BPS solitons that do not exist in the commutative limit.Comment: 17 pages, LaTeX2

Superconformal theories from Pseudoparticle Mechanics

We consider a one-dimensional Osp($N|2M$) pseudoparticle mechanical model which may be written as a phase space gauge theory. We show how the pseudoparticle model naturally encodes and explains the two-dimensional zero curvature approach to finding extended conformal symmetries. We describe a procedure of partial gauge fixing of these theories which leads generally to theories with superconformally extended ${\cal W}$-algebras. The pseudoparticle model allows one to derive the finite transformations of the gauge and matter fields occurring in these theories with extended conformal symmetries. In particular, the partial gauge fixing of the Osp($N|2$) pseudoparticle mechanical models results in theories with the SO($N$) invariant $N$-extended superconformal symmetry algebra of Bershadsky and Knizhnik. These algebras are nonlinear for $N \geq 3.$ We discuss in detail the cases of $N=1$ and $N=2,$ giving two new derivations of the superschwarzian derivatives. Some comments are made in the $N=2$ case on how twisted and topological theories represent a significant deformation of the original particle model. The particle model also allows one to interpret superconformal transformations as deformations of flags in super jet bundles over the associated super Riemann surface.Comment: 36 pages, UTTG-93-00

Symmetries of topological field theories in the BV-framework

Topological field theories of Schwarz-type generally admit symmetries whose algebra does not close off-shell, e.g. the basic symmetries of BF models or vector supersymmetry of the gauge-fixed action for Chern-Simons theory (this symmetry being at the origin of the perturbative finiteness of the theory). We present a detailed discussion of all these symmetries within the algebraic approach to the Batalin-Vilkovisky formalism. Moreover, we discuss the general algebraic construction of topological models of both Schwarz- and Witten-type.Comment: 30 page

Topological 2-form Gravity in Four Dimensions

A kind of topological field theory is proposed as a candidate to describe the global structure of the 2-form Einstein gravity with or without a cosmological constant. Indeed in the former case, we show that a quantum state in the candidate gives an exact solution of the Wheeler-DeWitt equation. The BRST quantization based on the Batalin-Fradkin-Vilkovisky (BFV) formalism is carried out for this topological version of the 2-form Einstein gravity.Comment: 15 page

A Superspace Formulation of The BV Action for Higher Derivative Theories

We first analyze the anti-BRST and double BRST structures of a certain higher derivative theory that has been known to possess BRST symmetry associated with its higher derivative structure. We discuss the invariance of this theory under shift symmetry in the Batalin Vilkovisky (BV) formalism. We show that the action for this theory can be written in a manifestly extended BRST invariant manner in superspace formalism using one Grassmann coordinate. It can also be written in a manifestly extended BRST invariant manner and on-shell manifestly extended anti-BRST invariant manner in superspace formalism using two Grassmann coordinates.Comment: accepted for publication in EPJ

Non Abelian Vortices as Instantons on Noncommutative Discrete Space

There seems to be close relationship between the moduli space of vortices and the moduli space of instantons, which is not yet clearly understood from a standpoint of the field theory. We clarify the reasons why many similarities are found in the methods for constructing the moduli of instanton and vortex, viewed in the light of the notion of the self-duality. We show that the non-Abelian vortex is nothing but the instanton in $R^{2} \times Z_{2}$ from a viewpoint of the noncommutative differential geometry and the gauge theory in discrete space. The action for pure Yang-Mills theory in $R^{2} \times Z_{2}$ is equivalent to that for Yang-Mills-Higgs theory in $R^{2}$.Comment: 19 pages, various arguments are added, the exposition is improve

Sum-over-histories origin of the composition laws of relativistic quantum mechanics and quantum cosmology

The scope of the paper has been broadened to include a more complete discussion of the following topics: The derivation of composition laws in quantum cosmology. The connection between the existence of a composition law in the sum over histories approach to relativistic quantum mechanics and quantum cosmology, and the existence of a canonical formulation.Comment: 36 page

3D collagen migration patterns reveal a SMAD3-dependent and TGF-β1-independent mechanism of recruitment for tumour-associated fibroblasts in lung adenocarcinoma

The TGF-β1 transcription factor SMAD3 is epigenetically repressed in tumour-associated fibroblasts (TAFs) from lung squamous cell carcinoma (SCC) but not adenocarcinoma (ADC) patients, which elicits a compensatory increase in SMAD2 that renders SCC-TAFs less fibrotic. Here we examined the effects of altered SMAD2/3 in fibroblast migration and its impact on the desmoplastic stroma formation in lung cancer.We used a microfluidic device to examine descriptors of early protrusions and subsequent migration in 3D collagen gels upon knocking down SMAD2 or SMAD3 by shRNA in control fibroblasts and TAFs.High SMAD3 conditions as in shSMAD2 fibroblasts and ADC-TAFs exhibited a migratory advantage in terms of protrusions (fewer and longer) and migration (faster and more directional) selectively without TGF-β1 along with Erk1/2 hyperactivation. This enhanced migration was abrogated by TGF-β1 as well as low glucose medium and the MEK inhibitor Trametinib. In contrast, high SMAD2 fibroblasts were poorly responsive to TGF-β1, high glucose and Trametinib, exhibiting impaired migration in all conditions.The basal migration advantage of high SMAD3 fibroblasts provides a straightforward mechanism underlying the larger accumulation of TAFs previously reported in ADC compared to SCC. Moreover, our results encourage using MEK inhibitors in ADC-TAFs but not SCC-TAFs.© 2022. The Author(s)