The Hilbert series of adjoint SQCD
TLDR
In this article, the authors use the plethystic exponential and the Molien-Weyl formula to compute the Hilbert series (generating functions), which counts gauge invariant operators in N = 1 supersymmetric SU (N c ), Sp (Nc ), SO (N C ) and G 2 gauge theories with 1 adjoint chiral superfield, fundamental chiral chiral fields, and zero classical superpotential.About:
This article is published in Nuclear Physics.The article was published on 2010-01-21 and is currently open access. It has received 83 citations till now. The article focuses on the topics: Hilbert–Poincaré series & Superpotential.read more
Citations
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The Hilbert series of the one instanton moduli space
TL;DR: In this paper, the moduli space of k G-instantons on Dp branes probing D(p + 4) branes in Type II theories is given by the Higgs branch of a supersymmetric gauge theory.
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Hilbert series for constructing Lagrangians: Expanding the phenomenologist’s toolbox
Landon Lehman,Adam Martin +1 more
TL;DR: In this article, the Hilbert series technique has been used for counting group invariants without derivatives in the context of constructing group-invariant Lagrangians, which is a useful cross-check on more well-known group theoretical methods.
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Low-derivative operators of the Standard Model effective field theory via Hilbert series methods
Landon Lehman,Adam Martin +1 more
TL;DR: In this paper, the authors explore an extension of Hilbert series techniques to count operators that include derivatives, and conjecture an algorithm that gives the number of invariant operators, properly accounting for redundancies due to the equations of motion and integration by parts.
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The Hilbert Series of the One Instanton Moduli Space
TL;DR: In this article, the moduli space of k G-instantons on R^4 is given by the Higgs branch of a supersymmetric gauge theory that lives on Dp branes probing D(p + 4) branes in Type II theories.
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Abelianization and sequential confinement in 2 + 1 dimensions
TL;DR: In this paper, the adjoint Lagrangian description of AD theories was studied in three dimensions, and it was shown that in the infrared it is equivalent to a linear quiver theory with one fundamental flavor.
References
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Book
Representation Theory: A First Course
TL;DR: This volume represents a series of lectures which aims to introduce the beginner to the finite dimensional representations of Lie groups and Lie algebras.
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Hilbert functions of graded algebras
TL;DR: In this article, the additive group of R has a direct-sum decomposition R = R + R, +..., where RiRi C R,+j and 1 E R,.
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Brane dynamics and gauge theory
TL;DR: In this article, the authors review some aspects of the interplay between the dynamics of branes in string theory and the classical and quantum physics of gauge theories with different numbers of supersymmetries in various dimensions.
Book
Computational Invariant Theory
Harm Derksen,Gregor Kemper +1 more
TL;DR: The second edition of this book provides a major update and covers many recent developments in the field of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision.
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Counting chiral primaries in N=1, d=4 superconformal field theories
TL;DR: In this article, the authors derived a procedure to count chiral primary states in N = 1 superconformal field theories in four dimensions, and the chiral primaries are counted by putting the N =1 field theory on S 3 × R.