Restricted Schur polynomials for fermions and integrability in the su(2|3) sector

Koch, Robert de Mello; Díaz, Pablo; Nokwara, Nkululeko

doi:10.1007/jhep03(2013)173

Cited by 35 publications

(54 citation statements)

References 72 publications

(113 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Schur polynomial basis constructed in [3] for a single adjoint scalar, diagonalizes the free field two point function and manifestly accounts for the trace relations that appear at finite N . In this section we will review the analogous construction, for a single adjoint fermion, given in [17].…”

Section: Schur Polynomials For Fermionsmentioning

confidence: 99%

Gauged fermionic matrix quantum mechanics

Berenstein

Koch

2019

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

We consider the gauged free fermionic matrix model, for a single fermionic matrix. In the large N limit this system describes a c = 1/2 chiral fermion in 1 + 1 dimensions. The Gauss' law constraint implies that to obtain a physical state, indices of the fermionic matrices must be fully contracted, to form a singlet. There are two ways in which this can be achieved: one can consider a trace basis formed from products of traces of fermionic matrices or one can consider a Schur function basis, labeled by Young diagrams. The Schur polynomials for the fermions involve a twisted character, as a consequence of Fermi statistics. The main result of this paper is a proof that the trace and Schur bases coincide up to a simple normalization coefficient that we have computed.

show abstract

Section: Schur Polynomials For Fermionsmentioning

confidence: 99%

Gauged fermionic matrix quantum mechanics

Berenstein

Koch

2019

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The most general operator will be constructed from adjoint scalars, adjoint fermions or covariant derivatives of these fields. The construction of restricted Schur polynomials with an arbitrary number of species of adjoint scalars and an arbitrary number of species of adjoint fermions was given in [46]. The construction of restricted Schur polynomials using covariant derivatives has been described in [47].…”

Section: Excitations Of Ads 5 ×Smentioning

confidence: 99%

Exciting LLM geometries

Koch

Huang

Tribelhorn

2018

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

We study excitations of LLM geometries. These geometries arise from the backreaction of a condensate of giant gravitons. Excitations of the condensed branes are open strings, which give rise to an emergent Yang-Mills theory at low energy. We study the dynamics of the planar limit of these emergent gauge theories, accumulating evidence that they are planar N = 4 super Yang-Mills. There are three observations supporting this conclusion: (i) we argue for an isomorphism between the planar Hilbert space of the original N = 4 super Yang-Mills and the planar Hilbert space of the emergent gauge theory, (ii) we argue that the OPE coefficients of the planar limit of the emergent gauge theory vanish and (iii) we argue that the planar spectrum of anomalous dimensions of the emergent gauge theory is that of planar N = 4 super Yang-Mills. Despite the fact that the planar limit of the emergent gauge theory is planar N = 4 super Yang-Mills, we explain why the emergent gauge theory is not N = 4 super Yang-Mills theory. 1 robert@neo.phys.wits.ac.za

show abstract

“…As a simple example, consider a scalar field Z which is an N × N matrix transforming in the adjoint representation of U(N). A complete set of operators built using three fields is given by {Tr(Z It is a highly non-trivial problem to write a basis of local operators that is not over complete at finite N. This problem has been solved for multimatrix models with U(N) gauge group in [1,2,3,4,5,6,7,8,9] and for single matrix models with SO(N) or Sp(N) gauge groups in [10,11,12]. The result of these studies is a basis of local operators that also diagonalizes the free field two point function.…”

Section: Discussionmentioning

confidence: 99%

“…Thus, we can form four adjoint fields φ IJ and our restricted Schur polynomials are labeled by 5 Young diagrams, one Young diagram r IJ for each field φ IJ and one which organizes the complete set of fields. According to [52,9] the number of restricted Schur polynomials at N = ∞ is given by expanding…”

Section: Situations Without New Finite N Relationsmentioning

confidence: 99%

FiniteNquiver gauge theory

2014

Self Cite

View full text Add to dashboard Cite

At finite N the number of restricted Schur polynomials is greater than or equal to the number of generalized restricted Schur polynomials. In this note we study this discrepancy and explain its origin. We conclude that, for quiver gauge theories, in general, the generalized restricted Shur polynomials correctly account for the complete set of finite N constraints and they provide a basis, while the restricted Schur polynomials only account for a subset of the finite N constraints and are thus overcomplete. We identify several situations in which the restricted Schur polynomials do in fact account for the complete set of finite N constraints. In these situations the restricted Schur polynomials and the generalized restricted Schur polynomials both provide good bases for the quiver gauge theory. Finally, we demonstrate situations in which the generalized restricted Schur polynomials reduce to the restricted Schur polynomials.

show abstract

Restricted Schur polynomials for fermions and integrability in the su(2|3) sector

Cited by 35 publications

References 72 publications

Gauged fermionic matrix quantum mechanics

Gauged fermionic matrix quantum mechanics

Exciting LLM geometries

FiniteNquiver gauge theory

Contact Info

Product

Resources

About