Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeSep 16th 2014
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexI've just finished a conference on [The Philosophical Foundations of Dualities in Physics](http://dualitiesblog.wordpress.com/), and had some questions on things spoken about. 1) Someone mentioned a 'parent action approach'. I can't see that nLab has anything on this, but maybe we have it under a different name. From [Parent Actions, Dualities and New Weyl-invariant Actions of Bosonic p-branes](http://arxiv.org/abs/hep-th/0301233), I see it's also called the 'master action'. Now, 'quantum master action' redirects to [[BV-BRST formalism]], where it speaks of a 'master equation'.

   I’ve just finished a conference on The Philosophical Foundations of Dualities in Physics, and had some questions on things spoken about.

   1) Someone mentioned a ’parent action approach’. I can’t see that nLab has anything on this, but maybe we have it under a different name. From Parent Actions, Dualities and New Weyl-invariant Actions of Bosonic p-branes, I see it’s also called the ’master action’. Now, ’quantum master action’ redirects to BV-BRST formalism, where it speaks of a ’master equation’.

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeSep 16th 2014
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItex2) Someone was talking about electric-magnetic duality as a forerunner of S-duality, and how instead of a picture with electrically charged particles, one could form a limit in terms of magnetically charged particles. This led to an idea that what is elementary in one picture can turn out to be composite in a dual picture. That reminded me of the Atiyah idea that involved in Montonen-Olive duality is the exchange of a gauge group and its Langlands dual. If we consider representations of such gauge groups, David Ben-Zvi once [told](http://golem.ph.utexas.edu/category/2010/08/what_is_the_langlands_programm.html#c034370) us that there's a correspondence between the irreps of a group and the conjugacy classes of its dual. Hmm, but do conjugacy classes count for anything physical. I see I didn't get an answer to my follow-up there: >if symmetric groups fall into this picture by being $GL(n,\mathbb{F}_1)$, and if GLs are Langlands self-dual, this explains how Young diagrams parameterize conjugacy classes and at the same time irreducible representations.

   2) Someone was talking about electric-magnetic duality as a forerunner of S-duality, and how instead of a picture with electrically charged particles, one could form a limit in terms of magnetically charged particles. This led to an idea that what is elementary in one picture can turn out to be composite in a dual picture.

   That reminded me of the Atiyah idea that involved in Montonen-Olive duality is the exchange of a gauge group and its Langlands dual. If we consider representations of such gauge groups, David Ben-Zvi once told us that there’s a correspondence between the irreps of a group and the conjugacy classes of its dual. Hmm, but do conjugacy classes count for anything physical.

   I see I didn’t get an answer to my follow-up there:

   if symmetric groups fall into this picture by being $GL(n,\mathbb{F}_1)$, and if GLs are Langlands self-dual, this explains how Young diagrams parameterize conjugacy classes and at the same time irreducible representations.

3. • CommentRowNumber3.
   • CommentAuthorJohn Dougherty
   • CommentTimeSep 16th 2014
   • PermaLink
   Author: John Dougherty
   Format: MarkdownItexI don't think the master action in the parent action approach is really related to the master equation of BV-BRST. From [Duality for the Non-Specialist](http://arxiv.org/abs/hep-th/9705122), it looks like the idea is that one can relate to Lagrangians $L_{1}$ and $L_{2}$ by coming up with a "master" or "parent" action that reduces to both $L_{1}$ and $L_{2}$ after varying some of the fields. The two ways of coming up with the parent action seem to be parametrizing the terms of $L_{1}$ and $L_{2}$ and adding terms that vanish off-shell. Then if you vary one of the new fields, you recover $L_{1}$, but if you vary another you recover $L_{2}$. So each of $L_{1}$ and $L_{2}$ can be seen as a "closure", in the computer programming sense, of your parent action.

   I don’t think the master action in the parent action approach is really related to the master equation of BV-BRST. From Duality for the Non-Specialist, it looks like the idea is that one can relate to Lagrangians $L_{1}$ and $L_{2}$ by coming up with a “master” or “parent” action that reduces to both $L_{1}$ and $L_{2}$ after varying some of the fields. The two ways of coming up with the parent action seem to be parametrizing the terms of $L_{1}$ and $L_{2}$ and adding terms that vanish off-shell. Then if you vary one of the new fields, you recover $L_{1}$, but if you vary another you recover $L_{2}$. So each of $L_{1}$ and $L_{2}$ can be seen as a “closure”, in the computer programming sense, of your parent action.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeSep 16th 2014
   • (edited Sep 16th 2014)
   • PermaLink
   Author: Urs
   Format: MarkdownItexYes, as John Dougherty says, there is no relation. (I wish people would strive to find better terminology...) The "parent action" refers to proving two Lagrangians to be classically equivalent by exhibiting both to be classically equivalent to a third one. The "BV-master equation" is just the condition for a certain differential to indeed square to zero. (The "master" here is an echo of the bewilderment about just how powerful homological algebra with its $d^2 = 0$ really is. On p. 25 of [[schreiber:What, and for what is Higher geometric quantization]] I am trying to use that to advertize that homotopy theory with its simplicial identities is much more masterly still ;-)

   Yes, as John Dougherty says, there is no relation. (I wish people would strive to find better terminology…)

   The “parent action” refers to proving two Lagrangians to be classically equivalent by exhibiting both to be classically equivalent to a third one.

   The “BV-master equation” is just the condition for a certain differential to indeed square to zero.

   (The “master” here is an echo of the bewilderment about just how powerful homological algebra with its $d^2 = 0$ really is. On p. 25 of What, and for what is Higher geometric quantization (schreiber) I am trying to use that to advertize that homotopy theory with its simplicial identities is much more masterly still ;-)

5. • CommentRowNumber5.
   • CommentAuthorDavid_Corfield
   • CommentTimeSep 17th 2014
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexTo get straight, when Miao and Ohta say >The parent or master action approach was proposed by Deser and Jackiw [1] nearly two decades ago, there's no relation to `quantum master action' on [[string field theory]] which links to [[BV-BRST formalism]]? Is disambiguation needed? Or maybe everyone opts for parent action now. In any case, is it worth having something on parent action?

   To get straight, when Miao and Ohta say

   The parent or master action approach was proposed by Deser and Jackiw [1] nearly two decades ago,

   there’s no relation to ‘quantum master action’ on string field theory which links to BV-BRST formalism?

   Is disambiguation needed? Or maybe everyone opts for parent action now.

   In any case, is it worth having something on parent action?

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeSep 17th 2014
   • (edited Sep 17th 2014)
   • PermaLink
   Author: Urs
   Format: MarkdownItexYes, there is no relation. I have started a bare minimum at _[[parent action functional]]_.

   Yes, there is no relation.

   I have started a bare minimum at parent action functional.

7. • CommentRowNumber7.
   • CommentAuthortonyjones
   • CommentTimeSep 17th 2014
   • PermaLink
   Author: tonyjones
   Format: Textare there any slides for these talks that will be made available? would be very interested to see them if possible

   are there any slides for these talks that will be made available? would be very interested to see them if possible
8. • CommentRowNumber8.
   • CommentAuthorDavid_Corfield
   • CommentTimeSep 20th 2014
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexTony, the talks were recorded. I'll report here if and when they're available. As for publishing, the idea is for the talk to be written up as papers and collected in a special edition of Studies in History and Philosophy of Modern Physics.

   Tony, the talks were recorded. I’ll report here if and when they’re available. As for publishing, the idea is for the talk to be written up as papers and collected in a special edition of Studies in History and Philosophy of Modern Physics.