Continuous Family of Conformal Field Theories and Exactly Marginal Operators

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Abstract
Does a conformal manifold imply the existence of exactly marginal operators? We answer this question affirmatively under the assumption that there exists a conformal interface with certain properties connecting nearby conformal field theories. We show that the exactly marginal operator that connects the conformal field theories can be reconstructed from the interface displacement operator. Our construction is model independent and based on the general principles of conformal symmetry.
Funding Information
  • Walter Burke Institute for Theoretical Physics
  • U.S. Department of Energy
  • Office of Science
  • High Energy Physics (DE-SC0011632)
  • Japan Society for the Promotion of Science (23K20046)
  • Japan Society for the Promotion of Science (23K03379)
  • Simons Foundation (MP-SIP-00005259)
  • Ministry of Education, Culture, Sports, Science and Technology
  • National Science Foundation (PHY-2309135)
  • National Science Foundation (PHY-1607611)
  • RIKEN
  • Ministero dell'Università e della Ricerca (D53C24005470001)
  • Instituto Nazionale di Fisica Nucleare
  • European Commission
  • HORIZON EUROPE Marie Sklodowska-Curie Actions (HORIZON-MSCA-2023-SE-01-101182937-HeI)
  • Leinweber Forum for Theoretical Physics
  • World Premier International Research Center Initiative

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