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Questions tagged [superconformality]

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2
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0answers
31 views

How to represent a superconformal algebra as differential operators acting on the fields in superspace?

Both super algebras and conformal algebras can be nicely represented as differential operators acting on the fields in superspace, but I've never seen one for superconformal algebras. I would ...
1
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0answers
48 views

Basic question about $\mathcal{N}=2$ SCFT

Consider a $\mathcal{N}=2$ SCFT radially quantized on $R^3 \times S^1$. The Lorentz group is $SU(2)_+ \times SU(2)_-$ and there are 8 independent supercharges $Q_{\alpha}^I,\tilde{Q}_{I \dot \alpha} $...
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0answers
47 views

Resource Recommendations: Extended Supersymmetry in 2+1 Dimensions

I'm interested in comprehensive resource recommendations covering extended supersymmetry (all cases) in 2+1 dimensions with the aim of understanding topics such as 2+1 dimensional SCFTs [ABJ(M), BLG ...
0
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1answer
85 views

Why doesn't the Superconformal Algebra close?

What I mean is, if I take the conformal algebra and the supersymmetry charges, how do I show that $[K, Q]$ is not in this algebra? I see this fact stated everywhere but with no proof. Any references ...
3
votes
1answer
179 views

Are there superconformal field theories in 10D?

I've heard that there is a belief that interacting conformal field theories do not exist in dimensions greater than 6, and in 6D the only known nontrivial CFTs are superconformal field theories. What ...
1
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0answers
69 views

Non-renormalization theorems at large N

I know of numerous examples of non-renormaliation theorems in theories with SUSY - e.g. the non-renormaliation of the superpotential in 4d theories. However, I've never seen a non-renormaliation ...
6
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1answer
264 views

Question about multiplets of 6d $\mathcal{N}=(1,0)$ SUSY

In Strathdeee's "Extended Poincare Supersymmetry", the first entry on page 16 lists the massless multiplets of 6d $\mathcal{N} = (1,0)$ supersymmetry as $2^2 = (2,1; 1) \oplus (1,1; 2)$. This is the ...
1
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0answers
58 views

Does scale invariance and R-invariance of Kähler potential imply superconformal symmetry?

Consider a four-dimensional $\mathcal{N} = 1$ field theory with Lagrangian: $ \mathcal{L} = \int d^4 \theta K(\Phi, \bar \Phi) $ and assume $K$ transforms well under dilations with scaling dimension ...
3
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1answer
230 views

Derivation of conformal generators in spinor helicity formalism

I've been trying for some time to find the expressions for conformal generators of Witten's paper in perturbative Yang-Mills. Given $P_{\alpha \dot{\alpha}} = \lambda_{\alpha} \overline{\lambda}_{\...
1
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0answers
90 views

Question about complex conjugation, and dotted/undotted indices in the 4d $\mathcal{N} = 1$ superconformal algebra

The 4-dimensional $\mathcal{N} = 1$ superconformal algebra as presented in equations (2.2, 2.3, and 2.4) of the paper, "Counting chiral primaries in N = 1 d = 4 superconformal algebras (arXiv:hep-th/...
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0answers
90 views

6D $(1,0)$ supersymmetry from properties of 6D spinors

It is known from string/M-theory considerations that six dimensional superconformal field theories exist with $(1,0)$ supersymmetry. But if one looks at Table 2.4 on page 47 of Sergio Cecotti's book,...
0
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1answer
54 views

Conformal supergravity or local tensor calculus? [closed]

What are the pros and cons of the two formalisms? In particular for explicit calculations of components. Are there textbooks providing self-contained, detailed description of superconformal ...
1
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0answers
37 views

On the action of superconformal generators in maximally supersymmetric Yang-Mills

Consider maximally supersymmetric Yang-Mills theory in 3+1 dimensions. This theory has 32 supercharges: 16 ordinary ones, conventionally labeled $Q$; and 16 superconformal ones, conventionally ...
3
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2answers
289 views

Question about the superconformal index

According to arXiv:1507.08553v1, the superconformal index, defined by $$I(\beta_j) = \mbox{Tr}_{\mathcal{H}}(-1)^F e^{-\gamma\{Q,Q^\dagger\}}e^{-\sum_{j}\beta_j t_j}$$ is independent of the ...
1
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1answer
59 views

Superconformal description of supergravity action

I've been reading this paper http://arxiv.org/abs/hep-th/0110263. In section 4, he discusses the benefits of writing the supergravity action in a superconformal way. I have a few questions regarding ...
0
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0answers
71 views

Diiference between three squashed sphere and three sphere and number of susy

First I know that three sphere $S^3$ and squashed sphere $S_b^3$ \begin{align} S_{b}^{3} = \begin{array} & R^2 \times S_{r}, \quad r=b, \quad b\rightarrow 0 \\ R^2 \times S_{r}, \quad r=\frac{1}{b}...
5
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0answers
281 views

Connection between the M5 brane and (2, 0) superconformal field theory

I have read that the worldvolume theory of the M5 brane is a $(2, 0)$ superconformal field theory (SCFT). But I have also learnt from talks that the $(2, 0)$ theory lacks a Lagrangian description. ...
4
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3answers
2k views

What does the $I$-$V$ curve in josephson junction mean?

According to the $I$-$V$ curve for Josephson junction tunneling for S-I-S (superconductor-insulator-superconductor), Do we have any tunneling current for $0< V\leq V_c$? If yes, then why don't we ...
5
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1answer
165 views

Why the bosonic part of the superconformal group $SU(2,2|1)$ is $SO(4,2) \times U(1)_R$?

Why in $d=4$ $\mathcal{N}=1$ SCFT the bosonic part of the superconformal group $SU(2,2|1)$ is $SO(4,2) \times U(1)_R$? More generally how can I determine the such a thing in other theories? Is there ...
4
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1answer
506 views

Questions on the $N=2$ superconformal algebra

In my understanding, mirror symmetry in physics originates from representation of the $N=2$ superconformal algebra. Why do we need precisely 2 supersymmetries (why not 1 or 4)? Moreover, a chiral (...
5
votes
1answer
214 views

Superconformal approach to supergravity

In the book (Supergravity - Daniel Z.Freedman & Antoine Van Proeyen - Cambridge), there is (Chapters 16-17) a presentation of pure supergravity or supergravity with matter, from a superconformal ...
8
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1answer
517 views

About the general expression of trace anomaly and CFT partition functions

I have put up a question here, https://mathoverflow.net/questions/139685/proof-of-the-general-expression-for-anomaly-in-a-cft-and-its-partition-function Here I am putting up a slightly different ...
11
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1answer
532 views

About defining “baryons” and “mesons”

I want to understand the proof of the claims (of the construction as well as of its uniqueness) of gauge singlet states given around equation 2.13 (page 10) of this paper. Also does the listing of ...
3
votes
1answer
261 views

Other Gross-Neveu like theories?

By "Gross-Neveu like" I mean non-supersymmetric QFTs whose partition function/beta-function (or any n-point function) is somehow exactly solvable in the large $N_c$ or $N_f$ or 't Hooft limit. (.....
9
votes
3answers
249 views

Embedding of $F(4)$ in $OSp(8|4)$?

Is the superconformal algebra in five dimensions, $F(4)$, a subalgebra of the (maximal) six-dimensional superconformal algebra $OSp(8|4)$?
4
votes
1answer
722 views

Boundary conditions in AdS/CFT

This question is in reference to this very famous paper of Witten. In general through the whole paper why is the author able to just focus on the scalar field propagating in the bulk and not need to ...
1
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0answers
126 views

Some questions about flavour and R-symmetry in $2+1$ ${\cal N}=3$ theory

I have heard this fact that for ${\cal N}=3$ theories in $2+1$ with $N_f$ ${\cal N}=3$ matter fields the flavour symmetry group is $USp(N_f)$, $U(N_f)$ or $SO(2N_f)$ depending on whether the gauge ...
2
votes
1answer
623 views

Pedagogic reference for calculation of 2-loop anomalous dimension (supersymmetric)

I want to know of pedagogic references which teach how to compute anomalous dimensions (..wave-function renormalization..) at lets say 2-loops. I guess there might be specialized techniques for ...
5
votes
1answer
285 views

About 2+1 dimensional superconformal algebra

I would like to get some help in interpreting the main equation of the superconformal algebra (in $2+1$ dimenions) as stated in equation 3.27 on page 18 of this paper. I am familiar with supersymmetry ...
5
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0answers
256 views

The ${\cal N} = 3$ Chern-Simons matter lagrangian

This question is sort of a continuation of this previous question of mine. I would like to know of some further details about the Lagrangian discussed in this paper in equation 2.8 (page 7) and in ...
3
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0answers
203 views

Some more questions on conformal spinors of $SO(n,2)$

This is somewhat of a continuation of my previous question. I had stated there that a conformal spinor ($V$) of $SO(n,2)$ can be created by taking a direct sum of two $SO(n-1,1)$ spinors $Q$ and $S$ ...
3
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1answer
251 views

Lorentz spinors of $SO(n,1)$ and conformal spinors of $SO(n,2)$

It would be great if someone can give me a reference (short enough!) which explains the (spinor) representation theory of the groups $SO(n,1)$ and $SO(n,2)$. I have searched through a few standard ...
7
votes
1answer
322 views

Reference for the ${\cal N}=3$ Chern-Simons Lagrangian at general $N_c$, $N_f$

I was wondering if someone could give me a reference where someone has explicitly written the Lagrangian for ${\cal N}=3$ $SU(N_c)$ Chern-Simons theory coupled to $N_f$ fundamental hypermultiplets. ...
4
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0answers
293 views

Central charge at the fixed point of the ${\cal N}=2$ Landau-Ginzburg theory in $1+1$ dimensions

Let me first believe that the ${\cal N}=2$ Landau-Ginzburg theory does in the IR flow to a non-trivial fixed point and that if the potential is of the form $\Phi ^k$ then the central charge of the CFT ...
2
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1answer
298 views

A certain $\cal{N}=2$ superconformal theory (or is it?)

I want to look at the following theory in $1+1$ dimensions with $\Phi$ being the chiral superfield, $L = \int d^2x d^4\theta \bar{\Phi}\Phi - \int d^2x d^2\theta \frac{\Phi^{k+2}}{k+2} - \int d^2x d^...
9
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1answer
201 views

Superconformal Multiplet Calculus in 6D

A convenient method for dealing with off-shell formulations of supergravity theories is provided by the superconformal multiplet calculus. This calculus was originally constructed for 4d ${\cal N}=2$ ...
6
votes
1answer
276 views

About unitarity and R-charge in 2+1 superconformal field theory

How does unitarity require that every scalar operator in a $2+1$ SCFT will have to have a scaling dimension $\geq \frac{1}{2}$ ? Why is an operator with scaling dimension exactly equal to $\frac{1}{2}...
2
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0answers
151 views

Argument for quantum theoretic conformality of $\cal{N}=2$ super-Chern-Simon's theory in $2+1$ dimensions -Part 2

This is in continuation to what I was asking here earlier - Argument for quantum theoretic conformality of $\cal{N}=2$ super-Chern-Simon's theory in $2+1$ dimensions Or one can look at this ...
2
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0answers
133 views

Some questions about chapter I.1 (by Minahan) of the “Review of AdS/CFT Integrability”

These questions are in reference to this beautiful review article by Minahan - http://arxiv.org/pdf/1012.3983v2 I gained a lot by reading some of its sections but not everything is clear to me. I ...