5,972 research outputs found
Spacetime and Physical Equivalence
In this essay I begin to lay out a conceptual scheme for: (i) analysing
dualities as cases of theoretical equivalence; (ii) assessing when cases of
theoretical equivalence are also cases of physical equivalence. The scheme is
applied to gauge/gravity dualities. I expound what I argue to be their
contribution to questions about: (iii) the nature of spacetime in quantum
gravity; (iv) broader philosophical and physical discussions of spacetime.
(i)-(ii) proceed by analysing duality through four contrasts. A duality will be
a suitable isomorphism between models: and the four relevant contrasts are as
follows:
(a) Bare theory: a triple of states, quantities, and dynamics endowed with
appropriate structures and symmetries; vs. interpreted theory: which is endowed
with, in addition, a suitable pair of interpretative maps.
(b) Extendable vs. unextendable theories: which can, respectively cannot, be
extended as regards their domains of application.
(c) External vs. internal intepretations: which are constructed,
respectively, by coupling the theory to another interpreted theory vs. from
within the theory itself.
(d) Theoretical vs. physical equivalence: which contrasts formal equivalence
with the equivalence of fully interpreted theories.
I apply this scheme to answering questions (iii)-(iv) for gauge/gravity
dualities. I argue that the things that are physically relevant are those that
stand in a bijective correspondence under duality: the common core of the two
models. I therefore conclude that most of the mathematical and physical
structures that we are familiar with, in these models, are largely, though
crucially never entirely, not part of that common core. Thus, the
interpretation of dualities for theories of quantum gravity compels us to
rethink the roles that spacetime, and many other tools in theoretical physics,
play in theories of spacetime.Comment: 25 pages. Winner of the essay contest "Space and Time After Quantum
Gravity" of the University of Illinois at Chicago and the University of
Genev
Dualities in persistent (co)homology
We consider sequences of absolute and relative homology and cohomology groups
that arise naturally for a filtered cell complex. We establish algebraic
relationships between their persistence modules, and show that they contain
equivalent information. We explain how one can use the existing algorithm for
persistent homology to process any of the four modules, and relate it to a
recently introduced persistent cohomology algorithm. We present experimental
evidence for the practical efficiency of the latter algorithm.Comment: 16 pages, 3 figures, submitted to the Inverse Problems special issue
on Topological Data Analysi
On the Worldsheet Derivation of Large N Dualities for the Superstring
Large N topological string dualities have led to a class of proposed
open/closed dualities for superstrings. In the topological string context, the
worldsheet derivation of these dualities has already been given. In this paper
we take the first step in deriving the full ten-dimensional superstring
dualities by showing how the dualities arise on the superstring worldsheet at
the level of F terms. As part of this derivation, we show for F-term
computations that the hybrid formalism for the superstring is equivalent to a
topological string in ten-dimensional spacetime. Using the description, we then show that the D brane boundary state for the
ten-dimensional open superstring naturally emerges on the worldsheet of the
closed superstring dual.Comment: 21 pages harvma
The mixed black hole partition function for the STU model
We evaluate the mixed partition function for dyonic BPS black holes using the
recently proposed degeneracy formula for the STU model. The result factorizes
into the OSV mixed partition function times a proportionality factor. The
latter is in agreement with the measure factor that was recently conjectured
for a class of N=2 black holes that contains the STU model.Comment: 14 page
- …