Conformal Bootstrap Approach to O(N) Fixed Points in Five
... scaling dimension is at ∆min (above the unitarity bound) and the second lowest scaling dimension is further gapped at ∆gap > ∆min . Again, borrowing the terminology of band theory, we refer ∆gap as the band-gap and ∆min as the mid-gap 2 . Applying the proposed two-gap approach, we found that the so ...
... scaling dimension is at ∆min (above the unitarity bound) and the second lowest scaling dimension is further gapped at ∆gap > ∆min . Again, borrowing the terminology of band theory, we refer ∆gap as the band-gap and ∆min as the mid-gap 2 . Applying the proposed two-gap approach, we found that the so ...
In order to integrate general relativity with quantum theory, we
... But while the known elementary particle states can easily be fit into this infinite array of spins and continuous masses, one has a vast overabundance of states as well as a lack of a dynamical theory of their interactions. One would like to have an algebraic structure that gave all possible particl ...
... But while the known elementary particle states can easily be fit into this infinite array of spins and continuous masses, one has a vast overabundance of states as well as a lack of a dynamical theory of their interactions. One would like to have an algebraic structure that gave all possible particl ...
Operator Product Expansion and Conservation Laws in Non
... time ago [1, 2] and was later analyzed in the context of string theory. Mehen, Stewart, and Wise explored the consequences of the conformal invariance for the scattering amplitudes involving unitarity fermions [3], and subsequently other applications have been considered in the literature [4–6]. The ...
... time ago [1, 2] and was later analyzed in the context of string theory. Mehen, Stewart, and Wise explored the consequences of the conformal invariance for the scattering amplitudes involving unitarity fermions [3], and subsequently other applications have been considered in the literature [4–6]. The ...
Nonabelions in the fractional quantum hall effect
... system which exhibit such a gap. In this paper, our goal is not to solve any particular hamiltonian, but to characterize the general properties such states must have if they exist. Accordingly, we will begin by assuming that we have an "incompressible F Q H E system" defined as follows. We take a sy ...
... system which exhibit such a gap. In this paper, our goal is not to solve any particular hamiltonian, but to characterize the general properties such states must have if they exist. Accordingly, we will begin by assuming that we have an "incompressible F Q H E system" defined as follows. We take a sy ...
Why we do quantum mechanics on Hilbert spaces
... Can be paraphrased as follows: “Any commuting C ∗ algebra is equivalent to an algebra of continuous functions from the character set of the algebra into the complex numbers”. A character of an abelian C ∗ -algebra is a ∗ -homomorphism of the algebra into the complex numbers. For a discussion of “cha ...
... Can be paraphrased as follows: “Any commuting C ∗ algebra is equivalent to an algebra of continuous functions from the character set of the algebra into the complex numbers”. A character of an abelian C ∗ -algebra is a ∗ -homomorphism of the algebra into the complex numbers. For a discussion of “cha ...
6. Edge Modes
... It’s tempting to say that this vanishes because it’s the integral of a total derivative. But if is compact, that’s no longer true. We have the possibility that winds some number of times as we go around the circle. For example, the configuration = 2⇡p /L is single valued for any integer p. Evaluated ...
... It’s tempting to say that this vanishes because it’s the integral of a total derivative. But if is compact, that’s no longer true. We have the possibility that winds some number of times as we go around the circle. For example, the configuration = 2⇡p /L is single valued for any integer p. Evaluated ...
In order to integrate general relativity with quantum
... mechanics. In previous work2, the author extended the Poincare Lie algebra to include a four-vector position operator as a natural covariant extension of the Poincare algebra to a larger Lie algebra of observables. This “Extended Poincare” (EP) Lie algebra also was shown to provide a more transparen ...
... mechanics. In previous work2, the author extended the Poincare Lie algebra to include a four-vector position operator as a natural covariant extension of the Poincare algebra to a larger Lie algebra of observables. This “Extended Poincare” (EP) Lie algebra also was shown to provide a more transparen ...
Intersection Between SFT and Condensed Matter
... Let us explore the implications of the linearity of the formula for the boundary state: Let us assume that the solution describes the ...
... Let us explore the implications of the linearity of the formula for the boundary state: Let us assume that the solution describes the ...
this PDF file - e
... obtain the corresponding central charge for NHEK geometry which is 12J. By using Cardy formula for entropy in CFT, we can recover the Bekenstein-Hawking entropy for Kerr black holes. Unlike the extremal case, the conformal symmetry in general (non-extremal) Kerr geometry is found from the solution s ...
... obtain the corresponding central charge for NHEK geometry which is 12J. By using Cardy formula for entropy in CFT, we can recover the Bekenstein-Hawking entropy for Kerr black holes. Unlike the extremal case, the conformal symmetry in general (non-extremal) Kerr geometry is found from the solution s ...
A pairing between super Lie-Rinehart and periodic cyclic
... We generalize this construction to the case of families, parameterized by commutative super-spaces, of noncommutative super-spaces, with the total space acted by super-Lie-Rinehart algebras over the base algebra, as follows: (L, R) - a Z/2-graded Lie-Rinehart algebra over a Z/2-graded-commutative ri ...
... We generalize this construction to the case of families, parameterized by commutative super-spaces, of noncommutative super-spaces, with the total space acted by super-Lie-Rinehart algebras over the base algebra, as follows: (L, R) - a Z/2-graded Lie-Rinehart algebra over a Z/2-graded-commutative ri ...
2006-11-14-RAL-Wang - Indico
... As well as causing quantum matter waves to lose coherence at small scales, the conformal gravitational field is responsible for cosmic acceleration linked to inflation and the problem of the cosmological constant. The formula for relating the measured decoherence of matter waves to spacetime fluct ...
... As well as causing quantum matter waves to lose coherence at small scales, the conformal gravitational field is responsible for cosmic acceleration linked to inflation and the problem of the cosmological constant. The formula for relating the measured decoherence of matter waves to spacetime fluct ...
An Integration of General Relativity and Relativistic Quantum
... The Lagrangian can be constructed as before but now with the new representations for Pb and ga . The dynamics would proceed by path-integral solutions and the energy momentum tensor would be computed from the dominant fields (which might just consist of the contribution from the massive sphere or bl ...
... The Lagrangian can be constructed as before but now with the new representations for Pb and ga . The dynamics would proceed by path-integral solutions and the energy momentum tensor would be computed from the dominant fields (which might just consist of the contribution from the massive sphere or bl ...
The notion of four-momentum in TGD
... 2. Does EP reduce to one aspect of QCC? This would require that classical Noether four-momentum identified as inertial momentum equals to the quantal four-momentum assignable to the states of super-conformal representations and identifiable as gravitational four-momentum. There would be only one ind ...
... 2. Does EP reduce to one aspect of QCC? This would require that classical Noether four-momentum identified as inertial momentum equals to the quantal four-momentum assignable to the states of super-conformal representations and identifiable as gravitational four-momentum. There would be only one ind ...
4. Introducing Conformal Field Theory
... Of course, we can alternate between thinking of theories as defined on fixed or fluctuating backgrounds. Any theory of 2d gravity which enjoys both diffeomorphism and Weyl invariance will reduce to a conformally invariant theory when the background metric is fixed. Similarly, any conformally invari ...
... Of course, we can alternate between thinking of theories as defined on fixed or fluctuating backgrounds. Any theory of 2d gravity which enjoys both diffeomorphism and Weyl invariance will reduce to a conformally invariant theory when the background metric is fixed. Similarly, any conformally invari ...
Classically conformal BL extended Standard Model
... problem that the quadratic divergence in quantum corrections to the Higgs self energy, which should be canceled by the Higgs mass parameter with extremely high precision when the cutoff scale is much higher than the electroweak scale. Λ:cutoff scale ...
... problem that the quadratic divergence in quantum corrections to the Higgs self energy, which should be canceled by the Higgs mass parameter with extremely high precision when the cutoff scale is much higher than the electroweak scale. Λ:cutoff scale ...
Whittaker Functions and Quantum Groups
... We will soon enter territory where each Cartan type must be handled individually, and although results are available for other Cartan types we will restrict ourselves to Type A, that is, GL(n). Here is the Casselman-Shalika formula for GL(n). (It was proved earlier by Shintani for this case.) If G = ...
... We will soon enter territory where each Cartan type must be handled individually, and although results are available for other Cartan types we will restrict ourselves to Type A, that is, GL(n). Here is the Casselman-Shalika formula for GL(n). (It was proved earlier by Shintani for this case.) If G = ...
LECTURES ON SYMPLECTIC REFLECTION ALGEBRAS Setting. W
... an isomorphism. Then we prove that the natural morphism RepΓ (H0,c , CΓ)// GL(CΓ)Γ → Spec(eH0,c e) is an isomorphism. Let y1 , . . . , yn be the tautological basis in Cn = h and x1 , . . . , xn be the dual basis in h∗ . The elements xn , yn still act on N Sn−1 ∼ = Cn . Show that [xn , yn ] ∈ O = {A| ...
... an isomorphism. Then we prove that the natural morphism RepΓ (H0,c , CΓ)// GL(CΓ)Γ → Spec(eH0,c e) is an isomorphism. Let y1 , . . . , yn be the tautological basis in Cn = h and x1 , . . . , xn be the dual basis in h∗ . The elements xn , yn still act on N Sn−1 ∼ = Cn . Show that [xn , yn ] ∈ O = {A| ...
Studying Quantum Field Theory
... decomposition into a positive and a negative frequency part. Adding the requirement of Hilbert space (or Wightman) positivity, i.e. demanding that the space generated by the action of a GCI (smeared quantum) field on the vacuum admits a (non-trivial) subspace realizing a unitary positive energy irre ...
... decomposition into a positive and a negative frequency part. Adding the requirement of Hilbert space (or Wightman) positivity, i.e. demanding that the space generated by the action of a GCI (smeared quantum) field on the vacuum admits a (non-trivial) subspace realizing a unitary positive energy irre ...
Gravity Duals for Nonrelativistic Conformal Field
... Discussion.—In discussions of AdS/CFT, one often hears that the CFT ‘‘lives at the boundary’’ of the bulk spacetime. The spacetime (2) is conformal to a pp-wave spacetime and hence has a boundary which is onedimensional —for z > 1, gtt grows faster than the other components at small r. While one mig ...
... Discussion.—In discussions of AdS/CFT, one often hears that the CFT ‘‘lives at the boundary’’ of the bulk spacetime. The spacetime (2) is conformal to a pp-wave spacetime and hence has a boundary which is onedimensional —for z > 1, gtt grows faster than the other components at small r. While one mig ...
on line
... groups are likewise defined by polynomial equations and have corresponding algebras C[G] , as well as versions k[G] defined over general fields with the same relations. Meanwhile, working over C , a “real form” means the additional structure of a compatible complex-linear involution making the coord ...
... groups are likewise defined by polynomial equations and have corresponding algebras C[G] , as well as versions k[G] defined over general fields with the same relations. Meanwhile, working over C , a “real form” means the additional structure of a compatible complex-linear involution making the coord ...
Gravity Duals for Nonrelativistic Conformal Field Theories Please share
... Discussion.—In discussions of AdS/CFT, one often hears that the CFT ‘‘lives at the boundary’’ of the bulk spacetime. The spacetime (2) is conformal to a pp-wave spacetime and hence has a boundary which is onedimensional —for z > 1, gtt grows faster than the other components at small r. While one mig ...
... Discussion.—In discussions of AdS/CFT, one often hears that the CFT ‘‘lives at the boundary’’ of the bulk spacetime. The spacetime (2) is conformal to a pp-wave spacetime and hence has a boundary which is onedimensional —for z > 1, gtt grows faster than the other components at small r. While one mig ...
Hawking Radiation by Kerr Black Holes and Conformal Symmetry Ivan Agullo,
... modes defining the jini j0i and jouti vacuum states are related by a conformal transformation. We can use expression (1) to evaluate this expectation value. Integrating by parts in (1) and taking into account that the field modes fiout vanish at spacelike infinity, one finds that the two-point fun ...
... modes defining the jini j0i and jouti vacuum states are related by a conformal transformation. We can use expression (1) to evaluate this expectation value. Integrating by parts in (1) and taking into account that the field modes fiout vanish at spacelike infinity, one finds that the two-point fun ...
Determinant formulas for the reflection equation algebra
... where Fσ : C → C op denotes the identity functor, equipped with a tensor structure σ, induces a functor from C C op -algebras to C-algebras, under which the REA is the image of the FRT algebra. 4. The center of REA The center of the FRT algebra has been thoroughly studied and described: it is isom ...
... where Fσ : C → C op denotes the identity functor, equipped with a tensor structure σ, induces a functor from C C op -algebras to C-algebras, under which the REA is the image of the FRT algebra. 4. The center of REA The center of the FRT algebra has been thoroughly studied and described: it is isom ...
A Conformal Field Theory Primer
... as we move them around each another. This in turn can be expressed very elegantly in terms of properties of a three-dimensional topological field theory, with remarkable consequences in knot theory. In understanding how all this works, a whole new algebraic structure of the operators, the fusion alg ...
... as we move them around each another. This in turn can be expressed very elegantly in terms of properties of a three-dimensional topological field theory, with remarkable consequences in knot theory. In understanding how all this works, a whole new algebraic structure of the operators, the fusion alg ...
Superintegrability as an organizing principle for special function theory
... possible, but of course not all commuting). If the independent symmetries can all be chosen of order k or less as differential operators the system is kth order superintegrable. Superintegrability is much more restrictive than integrability. Washington DC talk – p. 2/26 ...
... possible, but of course not all commuting). If the independent symmetries can all be chosen of order k or less as differential operators the system is kth order superintegrable. Superintegrability is much more restrictive than integrability. Washington DC talk – p. 2/26 ...