Katrina D. Barron
Ph.D. Rutgers University, 1996
Honors A.B. (in physics) University of Chicago, 1987
Algebra and Algebraic Geometry, Mathematical Physics
Vertex operator superalgebras and the algebraic and geometric foundations of superconformal field theory.
Conformal field theory (CFT), or more specifically, string theory, and related superconformal field theories (SCFTs) are the most promising attempts at developing a physical theory that combines all fundamental interactions of particles, including gravity. The “super” refers to an assumed symmetry between bosons (integral spin particles with symmetric wave functions) and fermions (half integral spin particles with anti-symmetric wave functions). For N=n SCFT, one assumes that each boson has n fermion superpartners.
The geometry of CFT and SCFT extends the use of Feynman diagrams, describing the interactions of point particles whose propagation in time sweeps out a line in space-time, to one-dimensional strings or superstrings whose propagation in time sweeps out a two-dimensional surface or supersurface called a “worldsheet”.
Much of my research involves the study of relationships between the worldsheet geometry of CFT and SCFT and properties of the algebras of correlation functions of the particle interactions.
- K. Barron, Automorphism groups of N=2 superconformal super-Riemann spheres, J. Pure Appl. Algebra, vol. 214 (2010), pp. 1973—1987.
- K. Barron, The moduli space of N=2 super-Riemann spheres with tubes, Commun. in Contemp. Math., vol. 9 (2007), pp. 857—940.
- K. Barron, Y.-Z. Huang, and J. Lepowsky, An equivalence of two constructions of permutation- twisted modules for lattice vertex operator algebras, J. Pure Appl. Algebra, Vol, 210 (2007), pp. 797—826.
- K. Barron, Superconformal change of variables for N=1 Neveu-Schwarz vertex operator superalgebras, J. of Algebra, Vol. 277 (2004), pp. 717—764.
- K. Barron, The moduli space of N=1 superspheres with tubes and the sewing operation, Memoirs Amer. Math. Soc., Vol. 162, no. 772, (2003).
- K. Barron, C. Dong, G. Mason, Twisted sectors for tensor product vertex operator algebras associated to permutation groups, Commun. in Math. Phys., Vol. 227 (2002), pp. 349—384.