670
Index
Verma modules
case G2, 220–223
definition, 220
Veronese sequence, 60
Vertex algebra (VA), 182
Vertex model, 16–17
Volume conjectures, 277
classical A-polynomial, 277–278
quantum, 278
and super-A-polynomials, 283–284
V R CKM parameters, 587–589, 591
W
W -algebras
AA, 182
CFT, 182
classical affine, 188
definition, 182
finite, 188
Hamiltonian reduction, 186, 187
Jacobson–Morozov Theorem, 187
PA, 182
physical call theories, 183
PVA, 183, 184
quantum affine, 188
toy model, 185, 186
VA, 184, 185
Warped extra-dimensions
Weakly Interacting Massive Particles
(WIMPs), 417, 418
Weierstrass elliptic function, 116
Weierstrass formula, 63–65
Weighted double Hurwitz numbers, 79
hypergeometric Toda t-functions, 81–82
Weighted Hurwitz numbers, 77–80
Weighted Newton’s Law, Gravitation
central force field, 504
diagonal covariance matrix, 503
dimensional analysis, 502
energy-momentum tensor, 504
energy priori probability density, 504
erfc potential, 505
4D pseudo-Euclidean static system, 502
gravitational potential, 505
linear radial gravitational field, 504
star formation, 502
unit-balancing constants, 502
Weight generating function
hypergeometric Toda t-functions, 81
Weight polytope, 289
Wess–Zumino–Novikov–Witten (WZNW)
model, 278–280
Weyl character formula, 287–289
lattice-polytope, 287
Weyl semimetal phase (WSM), 312, 314
Whittaker’s method, 491, 495
Wigner–Seitz radius, 361
Wilson lines
AdS 3 /CFT 2 , 403
bulk-to-bulk propagator, 405
Chern–Simons analogue, 404
Chern–Simons formulation, 403
Chern–Simons sector, 404
Chern–Simons theory, 403–405
coordinates, 403
correlators, 404
gauge-invariant, 403
higher spin notion, 404
holonomy conditions, 404
operator, 402
quantum corrections, 405
Virasoro conditions, 406
Wilson loop operator (WLO), 276
W R → eejj vs. W R mass, 590
W R → jj vs. W R mass, 590
W R → tb vs. W R mass, 589, 590
X
XMM-Newton X-ray observatory, 423
X-ray diffraction, 312
X-rays, 568, 570, 573
Y
Yukawa coupling, 340, 599, 601, 604
Z
Zamolodchikov W 3-algebra, 181
Zernike system
interbasis expansion coefficients, 175
separation of variables, 170
SO(4) Algebra, 169–170
3-sphere, SO(4), 171
two coordinate systems, S3, 172, 173
2-Sphere S2, 173, 174
Zero modes, 331
Zero-momentum particles, 422
Index
Verma modules
case G2, 220–223
definition, 220
Veronese sequence, 60
Vertex algebra (VA), 182
Vertex model, 16–17
Volume conjectures, 277
classical A-polynomial, 277–278
quantum, 278
and super-A-polynomials, 283–284
V R CKM parameters, 587–589, 591
W
W -algebras
AA, 182
CFT, 182
classical affine, 188
definition, 182
finite, 188
Hamiltonian reduction, 186, 187
Jacobson–Morozov Theorem, 187
PA, 182
physical call theories, 183
PVA, 183, 184
quantum affine, 188
toy model, 185, 186
VA, 184, 185
Warped extra-dimensions
Weakly Interacting Massive Particles
(WIMPs), 417, 418
Weierstrass elliptic function, 116
Weierstrass formula, 63–65
Weighted double Hurwitz numbers, 79
hypergeometric Toda t-functions, 81–82
Weighted Hurwitz numbers, 77–80
Weighted Newton’s Law, Gravitation
central force field, 504
diagonal covariance matrix, 503
dimensional analysis, 502
energy-momentum tensor, 504
energy priori probability density, 504
erfc potential, 505
4D pseudo-Euclidean static system, 502
gravitational potential, 505
linear radial gravitational field, 504
star formation, 502
unit-balancing constants, 502
Weight generating function
hypergeometric Toda t-functions, 81
Weight polytope, 289
Wess–Zumino–Novikov–Witten (WZNW)
model, 278–280
Weyl character formula, 287–289
lattice-polytope, 287
Weyl semimetal phase (WSM), 312, 314
Whittaker’s method, 491, 495
Wigner–Seitz radius, 361
Wilson lines
AdS 3 /CFT 2 , 403
bulk-to-bulk propagator, 405
Chern–Simons analogue, 404
Chern–Simons formulation, 403
Chern–Simons sector, 404
Chern–Simons theory, 403–405
coordinates, 403
correlators, 404
gauge-invariant, 403
higher spin notion, 404
holonomy conditions, 404
operator, 402
quantum corrections, 405
Virasoro conditions, 406
Wilson loop operator (WLO), 276
W R → eejj vs. W R mass, 590
W R → jj vs. W R mass, 590
W R → tb vs. W R mass, 589, 590
X
XMM-Newton X-ray observatory, 423
X-ray diffraction, 312
X-rays, 568, 570, 573
Y
Yukawa coupling, 340, 599, 601, 604
Z
Zamolodchikov W 3-algebra, 181
Zernike system
interbasis expansion coefficients, 175
separation of variables, 170
SO(4) Algebra, 169–170
3-sphere, SO(4), 171
two coordinate systems, S3, 172, 173
2-Sphere S2, 173, 174
Zero modes, 331
Zero-momentum particles, 422
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