Childers, Konner (2023) Duality and Categorical Equivalence: A Look at Gauge/Gravity. [Preprint]
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Abstract
It is well known among physicists that many distinct physical theories are equiva- lent, in that the state space of one can be formally mapped to the other (and vice versa). Yet this introduces a number of problems: what are the formal and conceptual criteria for theoretical equivalence? In other words, when do two distinct yet interchangeable mathematical structures represent the same physical system? Notice that difference in structure does not mean inequivalence of theories. Each involves difference in struc- ture. To complicate things further, theories can be dual to another theory. Duality is a special yet notably hard-to-define relationship. Although similar to theoretical equivalence, it remains unclear whether dual theories are another case of equivalence or stand as a unique type of theory relation. Indeed, “the complete physical meaning of the duality symmetry is still not clear, but a lot of work has been dedicated in recent years to understand the implications of this type of symmetry” (Alvarez- Gaume et al,“Duality in Quantum Field Theory and String Theory,”CERN). Perhaps the most extensive treatment of duality in philosophy of physics literature comes from De Haro and Butterfield, who argue that a) dual theories are not equivalent and b) formally, a duality is an isomorphism between models of the same theory. In this paper I iden- tify important problems with this view̶specifically, problems of bijective mappings between theory-models. To revise the account given by De Haro and Butterfield, I propose a category-theoretic account of duality in physics that qualifies as a specified form of so-called “categorical equivalence” for scientific theories. By introducing cat- egory theory as a formal framework, I show how these problems are avoided, while also demonstrating the extensive“reach”of this proposal by applying it to gauge/gravity.
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| Item Type: | Preprint | ||||||
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| Keywords: | duality, theoretical equivalence, AdS/CFT, holography | ||||||
| Subjects: | Specific Sciences > Physics Specific Sciences > Physics > Quantum Gravity Specific Sciences > Physics > Quantum Field Theory General Issues > Structure of Theories Specific Sciences > Physics > Symmetries/Invariances |
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| Depositing User: | Konner Childers | ||||||
| Date Deposited: | 08 Apr 2023 14:00 | ||||||
| Last Modified: | 08 Apr 2023 14:00 | ||||||
| Item ID: | 21975 | ||||||
| Subjects: | Specific Sciences > Physics Specific Sciences > Physics > Quantum Gravity Specific Sciences > Physics > Quantum Field Theory General Issues > Structure of Theories Specific Sciences > Physics > Symmetries/Invariances |
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| Date: | 17 February 2023 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/21975 |
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