In theoretical physics, modular invariance is the invariance under the group such as SL(2,Z) of large diffeomorphisms of the torus. The name comes from...

modular invariance of the torus one-point function. Due to remarkable identities of conformal blocks and structure constants, this modular invariance...

set A. Modular invariance — The partition function on the two-torus of the theory containing only the operators in A respects modular invariance. Starting...

CFT on all Riemann surfaces also requires modular invariance of the torus one-point function. Modular invariance of the torus partition function is therefore...

In physics and mathematics, continuous translational symmetry is the invariance of a system of equations under any translation (without rotation). Discrete...

particularly well-behaved, and are called regular. For example, Zhu's 1996 modular invariance theorem asserts that the characters of modules of a regular VOA form...

Department of Physics. p. 91. Dienes, Keith R. (7 November 1994), "Modular invariance, finiteness, and misaligned supersymmetry: New constraints on the...

ISSN 0370-1573. Giddings, Steven B.; Martinec, Emil; Witten, Edward (1986). "Modular invariance in string field theory". Physics Letters B. 176 (3–4). Elsevier BV:...

Virasoro algebra of this CFT. The proof of the above formula relies on modular invariance of a Euclidean CFT on the torus. The Cardy formula is usually understood...

A modular tensor category (also called a modular fusion category) is a type of tensor category that plays a role in the areas of topological quantum field...

anomalies must be canceled for a theory to be consistent. An example is modular invariance, the requirement of anomaly cancellation for a part of a global gravitational...

invariant under this group are then said to possess Poincaré invariance or relativistic invariance. 10 generators (in four spacetime dimensions) associated...

string spectra in cases where only closed strings are present via modular invariance. It did not lead to similar progress for models with open strings...

the SL(2, Z {\displaystyle \mathbb {Z} } )-invariance would not hold. In fact, there are no nontrivial modular forms of weight 2. Nevertheless, an analogue...

_{-1}(S)=\mu (S^{-1})\quad } then this is a right Haar measure. To show right invariance, apply the definition: μ − 1 ( S g ) = μ ( ( S g ) − 1 ) = μ ( g − 1 S...

Álvarez-Gaumé, Luis; Moore, Gregory; Vafa, Cumrun (1986). "Theta functions, modular invariance and strings". Communications in Mathematical Physics. 106 (1): 1–40...

Modified Newtonian dynamics Modified models of gravity Modular Neutron Array Modular invariance Modular ocean model Modulated ultrasound Modulation sphere...

groups. Modular forms are holomorphic automorphic forms defined over the groups SL(2, R) or PSL(2, R) with the discrete subgroup being the modular group...

is described by the modular S-matrix. Using the S-matrix, constraints on a CFT's spectrum can be derived from the modular invariance of the torus partition...

1007/BF02101810 Eholzer, Wolfgang; Skoruppa, Nils-Peter (1994-07-14), "Modular invariance and uniqueness of conformal characters", Communications in Mathematical...

Slodowy slice through f {\displaystyle f} . Zhu, Yongchang (1996). "Modular invariance of characters of vertex operator algebras". Journal of the American...

express Dyer's outer automorphism α {\displaystyle \alpha } of the extended modular group PGL(2, Z) in terms of the codenominator. This automorphism can be...

{1}{2\pi \alpha '}}} . I 0 {\displaystyle I_{0}} has diffeomorphism and Weyl invariance. Weyl symmetry is broken upon quantization (Conformal anomaly) and therefore...

trivially 1. Areas of all cusp neighborhoods are equal to this, by the invariance of the area under conjugation. Cusp form Fujikawa, Ege; Shiga, Hiroshige;...

but the effect of changing languages is bounded (a result called the invariance theorem, see below). There are two definitions of Kolmogorov complexity:...

iterations of the Sierpiński carpet. Due to their self-similarity and scale invariance, they easily accommodate multiple frequencies. They are also easy to fabricate...

many scales. Self-similarity is a typical property of fractals. Scale invariance is an exact form of self-similarity where at any magnification there is...

network architecture whose purpose is to 1) classify patterns with shift-invariance, and 2) model context at each layer of the network. It is essentially...

University Press Press. ISBN 978-0-19-063664-7. Lakoff, George (1990). "Invariance hypothesis: is abstract reasoning based on image-schemas?". Cognitive...

general result that follows from the hyperdeterminants product rule and invariance properties listed below is that the least common multiple of the dimensions...