By Lemma 6.2 wk (q) generate the ring of gauge invariant polynomials in q .
Solutions to WDVV from generalized Drinfeld-Sokolov hierarchies
Chiral rings, superpotentials and the vacuum structure of N = 1 supersymmetric gauge theories.
String Theory and the Vacuum Structure of Confining Gauge Theories
Chiral rings and anomalies in supersymmetric gauge theory.
String Theory and the Vacuum Structure of Confining Gauge Theories
Chiral rings and phases of supersymmetric gauge theories.
String Theory and the Vacuum Structure of Confining Gauge Theories
Perturbative construction of black rings is technically challenging in the presence of gauge ﬁelds and internal rotations9 .
G2 Dualities in D=5 Supergravity and Black Strings
This inductive deﬁnition makes sense more generally for any noetherian module over any ring (commutative or not); it can be viewed as a quantitative gauge of noetherianity.
The space of finitely generated rings
What are the natural observables of this integrable system? Going back to the underlying gauge theory description, the natural operators are those of the twisted chiral ring.
The Omega Deformation, Branes, Integrability, and Liouville Theory
The ﬁnite temperature potential – for the same set of states as we used in the CW piece – is then added, along with ring contributions for any bosonic ﬁelds whose mass is directly proportional to φ (i.e. gauge bosons).
Electroweak Baryogenesis in R-symmetric Supersymmetry
In some examples of ﬁrst class reductions to which the DS mechanism does not apply it has already been shown in that the ring of gauge invariant differential polynomials is not freely generated.
A Class of W-Algebras with Infinitely Generated Classical Limit
In this appendix we show that the generating set of the ring R of differential polynomials in L, I0, Z+, Z−, I− invariant under the gauge group (5.7) is given by (5.11-14) as stated in section 5.
A Class of W-Algebras with Infinitely Generated Classical Limit
Note that the ring corrections are the appropriate for this gauge choice.
Derivative expansion of quadratic operators in a general 't Hooft gauge
The dipole rings of are solutions of N = 1 d = 5 supergravity coupled to two vector multiplets, which is a theory with U (1)3 gauge group that can be obtained by consistent truncation of the maximal d = 5 supergravity theory.
Black Holes in Higher Dimensions
Turning to non-extremal solutions, one would certainly expect generalizations of the solutions of section 5.3 with non-trivial gauge ﬁelds. A solution describing a Myers-Perry black hole with a concentric dipole ring was presented in [133].
Black Holes in Higher Dimensions
If R = S/I is any quotient ring of S, then the S generator 1R of R induces a gauge δR, which we shall call the standard gauge on R = S/I (of course this depends on the presentation).
Test ideals via algebras of $p^{-e}$-linear maps
For example, in the previously mentioned example of Katzman [Kat09] of a ring where CR is not ﬁnitely generated it is easy to verify that the resulting pair (R, CR ) is gauge bounded.
Test ideals via algebras of $p^{-e}$-linear maps
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