<i>Lie Algebras in Particle Physics</i>

Slansky, R.

doi:10.1063/1.2915398

Cited by 137 publications

(212 citation statements)

References 0 publications

Supporting

Mentioning

209

Contrasting

Unclassified

Order By: Relevance

“…This leaves 2j + 1 columns with just one row; the symmetric combination of these obviously gives a state with spin j + 1/2. The computation of the degeneracy of this Young tableaux is then a simple application of the "factors over hooks" rule for the dimension of a representation [4]. This gives…”

Section: Expansion In Large Nc and N Fmentioning

confidence: 99%

Baryons and the phase diagram for a large number of colors and flavors

2008

View full text Add to dashboard Cite

We consider the possible phases of a non-Abelian gauge theory, as a function of temperature and quark chemical potential, when both the number of colors and flavors is very large. Generally, a large number of flavors washes out deconfining phase transitions. We show, however, that the degeneracy of even the lightest baryons is exponentially large. This implies that the baryon number (or fluctuations thereof, at zero chemical potential) is an order parameter in the limit of an infinite number of colors and flavors.

show abstract

Section: Expansion In Large Nc and N Fmentioning

confidence: 99%

Baryons and the phase diagram for a large number of colors and flavors

2008

View full text Add to dashboard Cite

show abstract

“…The only other non-trivial perturbations are when T a and T b are both type (2). For these perturbations, we have…”

Section: Perturbative Stabilitymentioning

confidence: 99%

“…where T a are the (traceless) generators of SU (N ) and will be taken to be in the Gell-Mann representation [2] and normalized so that…”

Section: The Modelmentioning

confidence: 99%

Class of kinks inSU(N)×Z2

Vachaspati

2001

Phys. Rev. D

View full text Add to dashboard Cite

In a classical, quartic field theory with SU (N ) × Z2 symmetry, a class of kink solutions can be found analytically for one special choice of parameters. We construct these solutions and determine their energies. In the limit N → ∞, the energy of the kink is equal to that of a kink in a Z2 model with the same mass parameter and quartic coupling (coefficient of Tr(Φ 4 )). We prove the stability of the solutions to small perturbations but global stability remains unproven. We then argue that the continuum of choices for the boundary conditions leads to a whole space of kink solutions. The kinks in this space occur in classes that are determined by the chosen boundary conditions. Each class is described by the coset space H/I where H is the unbroken symmetry group and I is the symmetry group that leaves the kink solution invariant. I. INTRODUCTIONClassical solutions in field theories have been of longstanding interest and have played an important role in our understanding of a variety of phenomena. The existence of solutions can be predicted on the basis of topology though the actual construction of the solutions is usually quite difficult and requires a certain amount of guesswork. Even after a solution is found, one needs to check its perturbative stability. And even after a solution is proved to be perturbatively stable, there is no guarantee that it is the globally stable solution.In this paper, we shall construct a class of kink solutions in purely scalar, SU (N ) × Z 2 field theories. The analytic construction is made possible by a special choice of parameters. We then prove the perturbative stability of the kink solutions. As there is no known extension of Bogomolnyi's method [1] to this case, global stability will remain unproven. We will then address the question of whether there might be other kink solutions in the model. We discuss the possibility that various boundary conditions imposed at spatial infinity, while topologically equivalent, lead to different kink solutions. Each kink solution is continuously degenerate with a degeneracy determined by the invariance group of the solution. We describe the problem of mapping the space of kink solutions.The following few sections deal with the construction and perturbative stability of the kink solutions that have been found. The space of kinks is described in Sec. VII and this can be read with minimal reference to the prior sections. II. THE MODELWe will consider the 1+1-dimensional, classical field theory(1)where Φ transforms in the adjoint representation of SU (N ) (N = 2n + 1) and hence is an N × N hermitian matrix. Φ can also be written in terms of components:where T a are the (traceless) generators of SU (N ) and will be taken to be in the Gell-Mann representation [2] and normalized so thatThe field components Φ a are real. The constant V 0 is chosen so that the minimum of the potential is at V = 0. Note the absence of a cubic term in the model. The center of SU (N ) is Z N and the group elements of the center transform Φ by multiplication by factors o...

show abstract

“…This equations reduce to Newton's gravitation law 50) in the limit of weak gravitation field and low motion [16].…”

Section: Einstein's Field Equationsmentioning

confidence: 99%

“…A very important result in group representation theory is Schur's Lemma [49,50]: If D(g) is a irreducible representation of a group G acting on a vector space V and if there is an operator A : V → V that commutes with all the elements of this representation, then A must be proportional to the identity of V . As a corollary, if there is a representation with an operator commuting with all elements of such representation but is not proportional to the identity then the representation is reducible.…”

Section: With D(g) † Being the Adjoint Of D(g)mentioning

confidence: 99%

Perturbações em torno de buracos negros e seus duais algébricos

Jimenez¹

View full text Add to dashboard Cite

To my beloved parents and grandma, they mean everything to me. To all my friends from Colombia, Brazil and other nationalities for the good moments shared together. I owe a special thanks to Daniel Morales and Javier Buitrago, for their kindness and for offering me their help when I first arrived at São Paulo.To the CPG staff and the secretaries at the DFMA for their good attention and help.Finally, I would like to thank FAPESP and CNPq for the financial support. ResumoNesta tese, nós estabelecemos algumas correspondências entre a dinâmica de campos escalares clássicos em certos espaço-tempos de fundo e duais algébricos apropriados. Os cenários estudados incluem soluções tipo buraco negro com constante cosmológica não nula e os espaços-tempos conhecidos como geometrias quase-extremas. Com base em várias propostas na literatura, associamos certos elementos próprios da dinâmica escalar a uma representação apropriada de uma álgebra relacionada com a invariância das equações de movimento escalar sob transformações conformes. Em particular, nós associamos representações de peso maior de dimensão infinita da álgebra sl(2, R) com modos e frequências quase-normais de campo escalar em geometrias quase-extremas e geometrias assintóticamente Anti de Sitter. AbstractIn this thesis, we establish some correspondences between dynamics of classical scalar fields in certain background spacetimes and appropriate algebraic duals. The scenarios studied include black hole solutions with non-zero cosmological constant and the spacetimes known as near extremal geometries. Based on several proposals in the literature, we associate certain elementsproper to scalar perturbative dynamics to an appropriated representation of an algebra related with the invariance of the scalar equations of motion under conformal transformations. In particular, we associate infinite dimensional highest weight representations of the algebra sl(2, R) to quasinormal modes and frequencies of scalar fields in near extremal geometries and asymptotically Anti de Sitter geometries.

show abstract

Lie Algebras in Particle Physics

Cited by 137 publications

References 0 publications

Baryons and the phase diagram for a large number of colors and flavors

Baryons and the phase diagram for a large number of colors and flavors

Class of kinks inSU(N)×Z2

Perturbações em torno de buracos negros e seus duais algébricos

Contact Info

Product

Resources

About