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Modular Invariance
, 2009
"... Two methods to prove the Riemann Hypothesis are presented. One is based on the modular properties of Θ (theta) functions and the other on the Hilbert–Polya proposal to find an operator whose spectrum reproduces the ordinates ρn (imaginary parts) of the zeta zeros in the critical line: sn = 1 +iρn. A ..."
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Two methods to prove the Riemann Hypothesis are presented. One is based on the modular properties of Θ (theta) functions and the other on the Hilbert–Polya proposal to find an operator whose spectrum reproduces the ordinates ρn (imaginary parts) of the zeta zeros in the critical line: sn = 1 +iρn
Modular invariants and subfactors
 Fields Institute Commun
"... Abstract. In this lecture we explain the intimate relationship between modular invariants in conformal field theory and braided subfactors in operator algebras. Our analysis is based on an approach to modular invariants using braided sector induction (“αinduction”) arising from the treatment of con ..."
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Cited by 16 (5 self)
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Abstract. In this lecture we explain the intimate relationship between modular invariants in conformal field theory and braided subfactors in operator algebras. Our analysis is based on an approach to modular invariants using braided sector induction (“αinduction”) arising from the treatment
MODULAR INVARIANT OF QUANTUM TORI
, 909
"... ABSTRACT. We define analogues of the classical Eisenstein series, Weierstrass function, Weierstrass equation and finally modular invariant for quantum tori. 1. ..."
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ABSTRACT. We define analogues of the classical Eisenstein series, Weierstrass function, Weierstrass equation and finally modular invariant for quantum tori. 1.
Modular Invariance and Nonrenormalizable Interactions
"... We examine the modular properties of nonrenormalizable superpotential terms in string theory and show that the requirement of modular invariance necessitates the nonvanishing of certain Nth order nonrenormalizable terms. In a class of models (free fermionic formulation) we explicitly verify that the ..."
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We examine the modular properties of nonrenormalizable superpotential terms in string theory and show that the requirement of modular invariance necessitates the nonvanishing of certain Nth order nonrenormalizable terms. In a class of models (free fermionic formulation) we explicitly verify
Modular invariants from subfactors
 QUANTUM SYMMETRIES IN THEORETICAL PHYSICS AND MATHEMATICS, EDITORS R.COQUEREAUX ET AL. CONTEMPORARY MATHEMATICS, AMS
, 2000
"... In these lectures we explain the intimate relationship between modular invariants in conformal field theory and braided subfactors in operator algebras. A subfactor with a braiding determines a matrix Z which is obtained as a coupling matrix comparing two kinds of braided sector induction (“αindu ..."
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Cited by 11 (2 self)
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In these lectures we explain the intimate relationship between modular invariants in conformal field theory and braided subfactors in operator algebras. A subfactor with a braiding determines a matrix Z which is obtained as a coupling matrix comparing two kinds of braided sector induction (“α
Chiral observables and modular invariants
 Commun. Math. Phys
, 2000
"... Abstract: Various definitions of chiral observables in a given Möbius covariant twodimensional (2D) theory are shown to be equivalent. Their representation theory in the vacuum Hilbert space of the 2D theory is studied. It shares the general characteristics of modular invariant partition functions, ..."
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Cited by 23 (3 self)
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Abstract: Various definitions of chiral observables in a given Möbius covariant twodimensional (2D) theory are shown to be equivalent. Their representation theory in the vacuum Hilbert space of the 2D theory is studied. It shares the general characteristics of modular invariant partition functions
QUANTIZATION ON THE TORUS AND MODULAR INVARIANCE
, 1999
"... The implementation of modular invariance on the torus as a phase space at the quantum level is discussed in a grouptheoretical framework. Unlike the classical case, at the quantum level some restrictions on the parameters of the theory should be imposed to ensure modular invariance. Two cases must ..."
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The implementation of modular invariance on the torus as a phase space at the quantum level is discussed in a grouptheoretical framework. Unlike the classical case, at the quantum level some restrictions on the parameters of the theory should be imposed to ensure modular invariance. Two cases must
Intertwining operators and modular invariance
, 2000
"... We extend Zhu’s theory to the case of intertwining operators of vertex operator algebra V. Namely, we show that the space of trace functions SI (u,τ) of intertwining operators I of type ( W U W satisfies modular invariance for each U and u ∈ U and we construct modular forms of vector type of rationa ..."
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Cited by 7 (0 self)
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We extend Zhu’s theory to the case of intertwining operators of vertex operator algebra V. Namely, we show that the space of trace functions SI (u,τ) of intertwining operators I of type ( W U W satisfies modular invariance for each U and u ∈ U and we construct modular forms of vector type
Modular invariance and characteristic numbers
 Commu.Math. Phys
, 1995
"... Abstract. We prove that a general miraculous cancellation formula, the divisibility of certain characteristic numbers and some other topological results are consequences of the modular invariance of elliptic operators on loop space. 1. Motivations In [AW], a gravitational anomaly cancellation formul ..."
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Cited by 19 (11 self)
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Abstract. We prove that a general miraculous cancellation formula, the divisibility of certain characteristic numbers and some other topological results are consequences of the modular invariance of elliptic operators on loop space. 1. Motivations In [AW], a gravitational anomaly cancellation
Modular Invariance and the Odderon
, 2008
"... We identify a new symmetry for the equations governing odderon amplitudes, corresponding in the Regge limit of QCD to the exchange of 3 reggeized gluons. The symmetry is a modular invariance with respect to the unique normal subgroup of SL(2, Z) of index 2. This leads to a natural description of the ..."
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We identify a new symmetry for the equations governing odderon amplitudes, corresponding in the Regge limit of QCD to the exchange of 3 reggeized gluons. The symmetry is a modular invariance with respect to the unique normal subgroup of SL(2, Z) of index 2. This leads to a natural description
Results 1  10
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73,691