OnS-duality in Abelian gauge theory View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1995-09

AUTHORS

E. Witten

ABSTRACT

U(1) gauge theory onR4 is known to possess an electric-magnetic duality symmetry that inverts the coupling constant and extends to an action ofSL(2,Z). In this paper, the duality is studied on a general four-manifold and it is shown that the partition function is not a modular-invariant function but transforms as a modular form. This result plays an essential role in determining a new low-energy interaction that arises whenN=2 supersymmetric Yang-Mills theory is formulated on a four-manifold; the determination of this interaction gives a new test of the solution of the model and would enter in computations of the Donaldson invariants of four-manifolds with b2+≤1. Certain other aspects of abelian duality, relevant to matters such as the dependence of Donaldson invariants on the second Stieffel-Whitney class, are also analyzed. More... »

PAGES

383-410

Journal

TITLE

Selecta Mathematica

ISSUE

2

VOLUME

1

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01671570

DOI

http://dx.doi.org/10.1007/bf01671570

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1004437611


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Institute for Advanced Study", 
          "id": "https://www.grid.ac/institutes/grid.78989.37", 
          "name": [
            "School of Natural Sciences, Institute for Advanced Study, Olden Lane, 08540, Princeton, NJ, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Witten", 
        "givenName": "E.", 
        "id": "sg:person.016240210261.17", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016240210261.17"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1016/0550-3213(94)90214-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1003449052"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0550-3213(94)90214-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1003449052"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0370-2693(77)90076-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021567237"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0370-2693(77)90076-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021567237"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0550-3213(94)90124-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1029241838"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0550-3213(94)90124-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1029241838"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0550-3213(94)90097-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1039866135"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0550-3213(94)90097-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1039866135"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0550-3213(89)90016-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044071549"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0550-3213(89)90016-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044071549"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0370-2693(88)90602-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044298643"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0370-2693(88)90602-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044298643"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0550-3213(82)90464-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1045177494"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0550-3213(82)90464-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1045177494"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0550-3213(92)90269-h", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1047744547"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0550-3213(92)90269-h", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1047744547"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0550-3213(82)90463-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1051171545"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0550-3213(82)90463-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1051171545"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0370-1573(94)90070-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1053013132"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0370-1573(94)90070-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1053013132"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0370-2693(86)90682-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1053463253"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0370-2693(86)90682-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1053463253"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4310/mrl.1994.v1.n6.a13", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1072461638"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1995-09", 
    "datePublishedReg": "1995-09-01", 
    "description": "U(1) gauge theory onR4 is known to possess an electric-magnetic duality symmetry that inverts the coupling constant and extends to an action ofSL(2,Z). In this paper, the duality is studied on a general four-manifold and it is shown that the partition function is not a modular-invariant function but transforms as a modular form. This result plays an essential role in determining a new low-energy interaction that arises whenN=2 supersymmetric Yang-Mills theory is formulated on a four-manifold; the determination of this interaction gives a new test of the solution of the model and would enter in computations of the Donaldson invariants of four-manifolds with b2+\u22641. Certain other aspects of abelian duality, relevant to matters such as the dependence of Donaldson invariants on the second Stieffel-Whitney class, are also analyzed.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/bf01671570", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1136551", 
        "issn": [
          "1022-1824", 
          "1420-9020"
        ], 
        "name": "Selecta Mathematica", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "1"
      }
    ], 
    "name": "OnS-duality in Abelian gauge theory", 
    "pagination": "383-410", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "152531532bff5c6dc9770a488bf0dd7f484e4641033f10227f244557682669af"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/bf01671570"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1004437611"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/bf01671570", 
      "https://app.dimensions.ai/details/publication/pub.1004437611"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-10T13:04", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8659_00000479.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007/BF01671570"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/bf01671570'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/bf01671570'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf01671570'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf01671570'


 

This table displays all metadata directly associated to this object as RDF triples.

97 TRIPLES      21 PREDICATES      39 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/bf01671570 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N462108ba370f4c239cfc6563daee239e
4 schema:citation https://doi.org/10.1016/0370-1573(94)90070-1
5 https://doi.org/10.1016/0370-2693(77)90076-4
6 https://doi.org/10.1016/0370-2693(86)90682-9
7 https://doi.org/10.1016/0370-2693(88)90602-8
8 https://doi.org/10.1016/0550-3213(82)90463-1
9 https://doi.org/10.1016/0550-3213(82)90464-3
10 https://doi.org/10.1016/0550-3213(89)90016-3
11 https://doi.org/10.1016/0550-3213(92)90269-h
12 https://doi.org/10.1016/0550-3213(94)90097-3
13 https://doi.org/10.1016/0550-3213(94)90124-4
14 https://doi.org/10.1016/0550-3213(94)90214-3
15 https://doi.org/10.4310/mrl.1994.v1.n6.a13
16 schema:datePublished 1995-09
17 schema:datePublishedReg 1995-09-01
18 schema:description U(1) gauge theory onR4 is known to possess an electric-magnetic duality symmetry that inverts the coupling constant and extends to an action ofSL(2,Z). In this paper, the duality is studied on a general four-manifold and it is shown that the partition function is not a modular-invariant function but transforms as a modular form. This result plays an essential role in determining a new low-energy interaction that arises whenN=2 supersymmetric Yang-Mills theory is formulated on a four-manifold; the determination of this interaction gives a new test of the solution of the model and would enter in computations of the Donaldson invariants of four-manifolds with b2+≤1. Certain other aspects of abelian duality, relevant to matters such as the dependence of Donaldson invariants on the second Stieffel-Whitney class, are also analyzed.
19 schema:genre research_article
20 schema:inLanguage en
21 schema:isAccessibleForFree false
22 schema:isPartOf N5716bfd0791048399446e6c9f307dc6b
23 Ne376f2f5865149c29df07b4d7c8e00ac
24 sg:journal.1136551
25 schema:name OnS-duality in Abelian gauge theory
26 schema:pagination 383-410
27 schema:productId N2cb4f641b56440a08c9a688df246c1d8
28 N5e102e3f1609447480015b4aa2b4c92a
29 N86df19d8bbd0488cac3ec9e0b66da51b
30 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004437611
31 https://doi.org/10.1007/bf01671570
32 schema:sdDatePublished 2019-04-10T13:04
33 schema:sdLicense https://scigraph.springernature.com/explorer/license/
34 schema:sdPublisher Nce0a0beaa61d45cbab1f88b146ddc4c2
35 schema:url http://link.springer.com/10.1007/BF01671570
36 sgo:license sg:explorer/license/
37 sgo:sdDataset articles
38 rdf:type schema:ScholarlyArticle
39 N2cb4f641b56440a08c9a688df246c1d8 schema:name readcube_id
40 schema:value 152531532bff5c6dc9770a488bf0dd7f484e4641033f10227f244557682669af
41 rdf:type schema:PropertyValue
42 N462108ba370f4c239cfc6563daee239e rdf:first sg:person.016240210261.17
43 rdf:rest rdf:nil
44 N5716bfd0791048399446e6c9f307dc6b schema:issueNumber 2
45 rdf:type schema:PublicationIssue
46 N5e102e3f1609447480015b4aa2b4c92a schema:name dimensions_id
47 schema:value pub.1004437611
48 rdf:type schema:PropertyValue
49 N86df19d8bbd0488cac3ec9e0b66da51b schema:name doi
50 schema:value 10.1007/bf01671570
51 rdf:type schema:PropertyValue
52 Nce0a0beaa61d45cbab1f88b146ddc4c2 schema:name Springer Nature - SN SciGraph project
53 rdf:type schema:Organization
54 Ne376f2f5865149c29df07b4d7c8e00ac schema:volumeNumber 1
55 rdf:type schema:PublicationVolume
56 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
57 schema:name Mathematical Sciences
58 rdf:type schema:DefinedTerm
59 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
60 schema:name Pure Mathematics
61 rdf:type schema:DefinedTerm
62 sg:journal.1136551 schema:issn 1022-1824
63 1420-9020
64 schema:name Selecta Mathematica
65 rdf:type schema:Periodical
66 sg:person.016240210261.17 schema:affiliation https://www.grid.ac/institutes/grid.78989.37
67 schema:familyName Witten
68 schema:givenName E.
69 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016240210261.17
70 rdf:type schema:Person
71 https://doi.org/10.1016/0370-1573(94)90070-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053013132
72 rdf:type schema:CreativeWork
73 https://doi.org/10.1016/0370-2693(77)90076-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021567237
74 rdf:type schema:CreativeWork
75 https://doi.org/10.1016/0370-2693(86)90682-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053463253
76 rdf:type schema:CreativeWork
77 https://doi.org/10.1016/0370-2693(88)90602-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044298643
78 rdf:type schema:CreativeWork
79 https://doi.org/10.1016/0550-3213(82)90463-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051171545
80 rdf:type schema:CreativeWork
81 https://doi.org/10.1016/0550-3213(82)90464-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045177494
82 rdf:type schema:CreativeWork
83 https://doi.org/10.1016/0550-3213(89)90016-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044071549
84 rdf:type schema:CreativeWork
85 https://doi.org/10.1016/0550-3213(92)90269-h schema:sameAs https://app.dimensions.ai/details/publication/pub.1047744547
86 rdf:type schema:CreativeWork
87 https://doi.org/10.1016/0550-3213(94)90097-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039866135
88 rdf:type schema:CreativeWork
89 https://doi.org/10.1016/0550-3213(94)90124-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029241838
90 rdf:type schema:CreativeWork
91 https://doi.org/10.1016/0550-3213(94)90214-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003449052
92 rdf:type schema:CreativeWork
93 https://doi.org/10.4310/mrl.1994.v1.n6.a13 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072461638
94 rdf:type schema:CreativeWork
95 https://www.grid.ac/institutes/grid.78989.37 schema:alternateName Institute for Advanced Study
96 schema:name School of Natural Sciences, Institute for Advanced Study, Olden Lane, 08540, Princeton, NJ, USA
97 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...