Questions tagged [superconformality]

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Control Parameter for Coulomb Phase of $\mathcal{N}=4$ SYM?

When discussing the vacua of $\mathcal{N}=4$ super-Yang-Mills (SYM) theory (with any connected gauge group you like, such as $U(N)$ or $SU(N)$), a simple analysis of the potential tells you the vacuum ...
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47 views

Intuition for Plethystic Exponentiation

I have been studying Abjit Gadde's lecture notes on the superconformal index, and I can't seem to understand what the intuition for the plethystic exponentiation is. He motivates it with the ...
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1answer
102 views

Why study 6d SCFT, when it is 2d CFT that is well studied?

According to AGT correspondence, if we compactify 6d SCFT to a 4d Riemann surface, then we find that certain physical quantities of 4d QFT on this surface are related to certain properties of that ...
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1answer
60 views

Worldsheet SCFT on a lattice

My question is clear from the title. I'm curious whether it is possible to put the string world sheet SCFT on a lattice. I expect when the world sheet theory is chiral, then it's not possible. But I ...
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62 views

What Operator is the Superconformal Index Counting?

Given a differential operator $\mathcal{D}$ with adjoint $\mathcal{D}^\dagger$, the analytical index of $\mathcal{D}$ is usually defined by $$\text{ind }\mathcal{D}=\dim\ker\mathcal{D}-\dim\ker\...
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1answer
56 views

Superconformal transformation (Polchinski text 12.3.8)

I am reading Polchinski's text book STING THEORY. In the above of eq.(12.3.8), the differential $D_\theta = \partial_\theta + \theta\partial_z$ is defined and \begin{equation} D_\theta = D_\theta\...
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31 views

On the picture of Schur limit of the superconformal index

My goal is to understand qualitatively (hopefully quantitatively in future) the existence of the relationship of the Schur limit of the superconformal index given by \begin{align} \mathcal{I}(q)=\...
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1answer
92 views

Weyl SUSY vs Conformal SUSY

Is it possible to add the generators of dilatations to Poincare superalgebra in any dimensions with any number of supercharges without adding the full superconformal generators? I have only seen ...
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1answer
170 views

6D (2,0) superconformal field theory

I'm looking for a good reference book or textbook to study on 6D (2,0) superconformal field theory as a part of string theory.
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36 views

$(0,2)$ worldsheet SUSY implies ${\cal N}=1$ spacetime SUSY (reference request)

In [1] they write that "Boucher et al. [14] found quite generally that $(0, 2)$ world-sheet SUSY ensures the existence of $N = 1$ spacetime SUSY." But this reference "[14]" they cite just says: "...
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98 views

Supercurrent of the $bc$-$\beta\gamma$ SCFT

In Polchinksi's Sec. 10.1, the $bc$-$\beta\gamma$ SCFT is introduced with action $$S_{BC} = \frac{1}{2\pi} \int d^2z (b \bar \partial c + \beta \bar \partial \gamma)$$ and supercurrent $$T_F = -\...
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38 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 ...
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69 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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53 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 ...
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1answer
126 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 ...
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1answer
308 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 ...
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82 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 ...
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393 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 ...
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62 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 ...
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1answer
358 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}_{\...
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138 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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1answer
193 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,...
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1answer
64 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 ...
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40 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 ...
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2answers
461 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 ...
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1answer
73 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 ...
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78 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}...
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344 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. ...
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4answers
4k 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 ...
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1answer
229 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 ...
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557 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 (...
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1answer
263 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 ...
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645 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 ...
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1answer
559 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 ...
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1answer
274 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. (.....
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3answers
261 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 $OSp(8|4)$?
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820 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 ...
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147 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 ...
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1answer
692 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 ...
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1answer
296 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 ...
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265 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 ...
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209 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 $S$ ...
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1answer
274 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 ...
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340 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. ...
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310 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 ...
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1answer
332 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^...
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1answer
227 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 ${\cal N}=2$ ...
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289 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}...
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152 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 ...
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143 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 ...