superalgebra and (synthetic ) supergeometry
What is called picture number in string theory is a certain grading originally seen in the quantization of the NSR superstring (Friedan-Martinec-Shenker 86).
The supergeometric meaning was clarified in Belopolsky 97b in terms of an extra grading on differential forms on supermanifolds induced from a choice of integral top-form needed for a notion of integration over supermanifolds, see Catenacci-Grassi-Noja 18
The appearance in the quantization of the NSR superstring is due to
A supergeometric interpretation of picture changing operators as part of the geometry of super Riemann surfaces is given in
Alexander Belopolsky, New Geometrical Approach to Superstrings (arXiv:hep-th/9703183)
Alexander Belopolsky, Picture changing operators in supergeometry and superstring theory (arXiv:hep-th/9706033)
further amplified in
In this perspective picture number is an extra grading on differential forms on supermanifolds induced from a choice of integral top-form needed to define integration over supermanifolds:
Roberto Catenacci, Pietro Grassi, S. Noja, Superstring Field Theory, Superforms and Supergeometry, Journal of Geometry and Physics Volume 148, February 2020, 103559 (arXiv:1807.09563)
(with an eye towards superstring field theory)
Carlo A. Cremonini, Pietro Grassi, Pictures from Super Chern-Simons Theory (arXiv:1907.07152)
(with an eye towards super Chern-Simons theory)
Carlo A. Cremonini, The Geometry of Picture Changing Operators [arXiv:2305.02828]
Review:
See also:
Via pure spinors:
Last revised on February 20, 2024 at 05:26:27. See the history of this page for a list of all contributions to it.