5,781 reputation
1445
bio website ncatlab.org/nlab/show/…
location
age 93
visits member for 2 years, 9 months
seen 13 hours ago

I am a postdoc in mathematics, but have my degree in theoretical physics. My work is about mathematical structures motivated from quantum field theory and string theory. For more see my personal web on the nLab.


Jul
3
awarded  Announcer
Jun
3
awarded  quantum-field-theory
Jun
2
answered TQFT associates a category to a manifold
May
28
awarded  Necromancer
May
15
awarded  Nice Answer
May
9
answered Gravitational Chern-Simons theory for bosons and fermions
May
7
awarded  Nice Answer
Apr
11
awarded  Good Answer
Apr
7
awarded  Announcer
Apr
7
revised p-Adic String Theory and the String-orientation of Topological Modular Forms (tmf)
fixed another trivial typo
Apr
7
answered “tmf$(n)$ is the space of supersymmetric conformal field theories of central charge $-n$”
Apr
7
asked p-Adic String Theory and the String-orientation of Topological Modular Forms (tmf)
Mar
25
comment What are type system examples of local gauge transformation- and field strength-like objects?
To answer your question: yes, in HoTT there are gauge transformations, which are not present in an ordinary topos. For instance in cohesive HoTT there is a type BU(1)_conn of electromagnetic gauge fields. This does not exists in any plain topos (1-topos). For X a manifold, then a function X --> BU(1)_conn is an electromagnetic gauge field on X and a homotopy between two such maps is a gauge transformation between these field configurations. This gauge/homotopy theoretic aspect is not present in an ordinary topos.
Mar
23
answered What are type system examples of local gauge transformation- and field strength-like objects?
Mar
20
awarded  Necromancer
Mar
20
comment The physics community's take on noncommutative geometry
I just see that an earlier reference that highlights that the particle limit of the superstring's SCFT is a spectral triple are these lecture notes: Jürg Fröhlich, Krzysztof Gawędzki, "Conformal Field Theory and Geometry of Strings", extended lecture notes for lecture given at the Mathematical Quantum Theory Conference, Vancouver, Canada, August 4-8 arxiv.org/abs/hep-th/9310187 . They explicitly spell out a bunch of examples.
Mar
19
answered The physics community's take on noncommutative geometry
Mar
7
comment Why am I wrong about how to view gauge theory?
@drake: locally every gauge transformation is small (for a connected gauge group), so already quotienting out small gauge transformations destroys locality.
Mar
7
awarded  Announcer
Mar
7
comment Why am I wrong about how to view gauge theory?
@Jia Yiyang, I see, right, I have edited the reply above to include now a point (5) that makes the relation to the construction that the OP considers more explicit.