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Langlands Duality and Quantum Field Theory.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Langlands Duality and Quantum Field Theory./
作者:	Yoo, Philsang.
面頁冊數:	1 online resource (335 pages)
附註:	Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.
Contained By:	Dissertation Abstracts International78-10B(E).
標題:	Mathematics. -
電子資源:	click for full text (PQDT)
ISBN:	9781369818666

Langlands Duality and Quantum Field Theory.
Yoo, Philsang.

Langlands Duality and Quantum Field Theory. - 1 online resource (335 pages)

Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

Langlands duality appears in several different areas of mathematics and physics. In this thesis, we take the first steps to realizing Langlands duality in quantum field theory in terms of rigorous mathematics and finding applications of the QFT perspective back to mathematics. This consists of three related pieces of work. First, we analyze topological twists of certain 4-dimensional supersymmetric gauge theory studied by Kapustin and Witten using derived algebraic geometry and find algebraic structures of interest in the geometric Langlands program. In particular, we establish the unexpected claim that a topological twist can still retain a subtle algebraic structure. Second, we recover Arinkin and Gaitsgory's modified conjecture by requiring compatibility with a vacuum state. Moreover, we conjecture and provide evidence for a new gauge symmetry breaking result and further suggest a factorization structure relating geometric Langlands for different groups in a curious way. Finally, we develop a general framework of degenerate field theories which do not necessarily admit a Lagrangian description. This allows one to look for many more new instances of Langlands duality appearing in QFT.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369818666Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Langlands Duality and Quantum Field Theory.
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100 1 $a Yoo, Philsang. $3 1180733
245 1 0 $a Langlands Duality and Quantum Field Theory.
264 0 $c 2017
300 $a 1 online resource (335 pages)
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500 $a Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.
500 $a Adviser: Kevin Costello.
502 $a Thesis (Ph.D.) $c Northwestern University $d 2017.
504 $a Includes bibliographical references
520 $a Langlands duality appears in several different areas of mathematics and physics. In this thesis, we take the first steps to realizing Langlands duality in quantum field theory in terms of rigorous mathematics and finding applications of the QFT perspective back to mathematics. This consists of three related pieces of work. First, we analyze topological twists of certain 4-dimensional supersymmetric gauge theory studied by Kapustin and Witten using derived algebraic geometry and find algebraic structures of interest in the geometric Langlands program. In particular, we establish the unexpected claim that a topological twist can still retain a subtle algebraic structure. Second, we recover Arinkin and Gaitsgory's modified conjecture by requiring compatibility with a vacuum state. Moreover, we conjecture and provide evidence for a new gauge symmetry breaking result and further suggest a factorization structure relating geometric Langlands for different groups in a curious way. Finally, we develop a general framework of degenerate field theories which do not necessarily admit a Lagrangian description. This allows one to look for many more new instances of Langlands duality appearing in QFT.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Northwestern University. $b Mathematics. $3 1180604
773 0 $t Dissertation Abstracts International $g 78-10B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10279141 $z click for full text (PQDT)