Questions tagged [supersymmetry]

A postulated symmetry between bosonic and fermionic fields in quantum field theories and string theories.

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No-go theorem evasion for higher spin (super)string theory

The inclusion of (conventional) SUSY truncates spin states in (super)string theory and M-theory. My question here is the following: could a non-standard SUSY algebra be constructed in such a way (...
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Why for 6d SCFT we consider (1,0) and (2,0) only?

It is known to have a stress-energy tensor we must have the supercharges $\mathcal{N}<2$. My confusion is why in most cases we consider chiral supercharges, and what is the problem with $\mathcal{N}...
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Question on the life-time of a super-symmetric particle [duplicate]

I was watching a random video on SUSY. In the video, they were discussing that SUSY explains dark matter. That DM is probably a SUSY particle. How is this possible? We know that the life of a Top ...
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Abelian Gauge Theory

Hello everyone I have a question on this exercise from my Supersymmetry class in 4d ${\cal N}=1$. Given a $\text{U}(1)^3$ gauge theory with 9 chirals $A_i , B_j , C_k$ with $i,j,k$ running from 1 to 3 ...
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General derivation of Supervirasoro algebra

I'm looking for a derivation derivation of the ($\mathcal{N} = 1$) Supervirasoro algebra (NS sector) that does't just apply to specific examples. Most books/papers either just cite the result, or ...
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Can any other manifold be used for compactifying the 6 extra dimensions of string theory? [duplicate]

I'm a layman interested in string theory. I read about how the 6 extra dimensions of superstring theory are compactified into 3-dimensional complex manifolds (so real dimension 6?) called Calabi-yau ...
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Why is (1,1) worldsheet SUSY enhanced to (2,2) SUSY after compactification of type II string theory on a CY threefold?

I have a quick question. In case of compactification on an Calabi Yau cutting off 3/4th SUSY from the type-II string in 10D leads to an enhancement of worldsheet SUSY. It has been claimed since time ...
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How does SUSY differ from just having standard model (SM) particles in new Lorentz Group representations?

Under the standard model (SM), it is the irreducible representations of the Lorentz group which allows us to classify particles according to their spin. We can then further label particles using the ...
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Dimension of moduli space for SQCD

We are in $\mathcal{N}=1$ SUSY. Consider massless SQCD with gauge group $SU(N)$ and $F$ flavours. The quarks superfields $Q$ and $\tilde{Q}$ are $F\times N$ and $N\times F$ matrices respectively and ...
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Functional integral for unconstrained superfields

Context In this paper by Srivastava (also in his book "Supersymmetry, Superfields and Supergravity"), he proposes the functional integral for a chiral superfield $\Phi$. In order to work ...
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Translating an $\mathcal{N}=2$ quiver into an $\mathcal{N}=1$ one

I am quite new to quivers and I was wondering what does the $\mathcal{N}=2$ quiver (in 4d SUSY) look like in $\mathcal{N}=1$ language? I know that the $\mathcal{N}=2$ vplet gives an $\mathcal{N}=1$ ...
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Generating functional for a chiral superfield

In this paper by Petrov, he writes the action of the Wess-Zumino model for a chiral superfield $$S_J[\Phi,\bar\Phi,J,\bar J]=\int d^6z \Bigg(\frac{1}{2}\Phi\left(-\frac{\bar D^2}{4}\right)\bar\Phi+\...
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Parametrization of classical moduli space for SUSY QED

A bit of context I'm following Bertolini's notes on SUSY and in section 5.3.1 he claims that, for a SUSY theory without superpotential, i.e. in which the $D$-flat directions coincides with the moduli ...
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Are there examples of harmonic differential forms in non-singular projective algebraic varieties that appear in general relativity or quantum physics?

I would like to study some real physical examples of harmonic differential forms in non-singular projective algebraic varieties. As Calabi - Yau and Kahler manifolds are used in supersymmetry theories ...
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Problem in deriving equations of motion for a free chiral superfield

Setting of the problem We are in $\mathcal{N}=1$ SUSY and we are using superspace formalism in the set of coordinates $(x^\mu,\theta_\alpha,\bar\theta_{\dot{\alpha}})$ where $\theta_\alpha$ and $\bar\...
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One-Loop Fayet-Iliopoulos term in heterotic string

I'm having problems computing the coefficient of the Fayet-Iliopoulos term, following the book of Kiritsis. With the term in the effective action in the Einstein Frame $$- \frac{\zeta}{2}M_s ^2 \int \...
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SUSY vs bosonization and fermionization

(New to the concepts.) From what was known SUSY described a theory consisted of both a boson and a fermion pair as a symmetric counter part. Bosonization and Fermionization on the other hand described ...
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Is there a guide for superconformal field theories?

Is there a guide for superconformal field theories for $\mathcal N=1,2,3,4…$ ? I don't understand what characteristics they have, what the motivation for each is, and how they relate to supergravity ...
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How to identify the dyon being condensated at the ${\cal N}=2$ SUSY $u$-plane?

For the $u$-plane monodromy at $u=u_0$ $$\mathcal{M}^{p,q}=\begin{pmatrix} 1+pq & p^2 \\ -q^2 & 1-pq \\ \end{pmatrix}$$ the statement is that dyons with electric and magnetic charges $(p,q)$ ...
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Doubt on dotted indices notation for Weyl spinors

I'm starting Bailin and Love "Supersymmetric gauge field theory and string theory" and trying to get used to dotted indices. Let's consider a Dirac spinor written in terms of left and right ...
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What anticommutes in the two-component formalism for spinors?

I'm studying the 2-component (alias Pauli) formalism for spinors, and I'm confused with the anticommutativity of the objects it uses and describes. For "objects" i mean the spinors $\chi_\...
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MSSM interactions

I have seen many pictures of fermion-boson interactions. But none of them are related to gravitons and MSSM particles. Do gravitons interact with photons, gluons and other particles? What about the 4 ...
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Anti-de Sitter superalgebra from preserved symmetry

Following Freedman & Van Proeyen's "Supergravity", the $\mathcal{N}=1,\, D=4$ AdS supergravity action is $$ \dfrac{1}{2\kappa^2}\int d^4x \; e \left[R(\omega) - \bar{\psi}_\mu \gamma^{\...
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Infinite set of scalar fields in extended SUSY theories

When dealing with extended SUSY theories (i.e. $\mathcal{N}>1$) it is generally affirmed that to build a correct off-shell Lagrangian one needs to introduce an infinite set of auxiliary fields to ...
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How do central charges affect $R$-symmetry group in extended SUSY?

When examining a ${\cal N}=1$ SUSY one finds that the corresponding $R$-symmetry group is simply $U(1)$. On the other hand, when considering extended SUSY (i.e. ${\cal N}>1$) the largest possible ...
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Is there a room for "another SUSY" to reduce extra dimensions?

I've heard that supersymmetry already dropped dimensions count in String theories from 26 to 10 (11 - after Witten). So, is there any space left in the rest of the math to introduce some "another ...
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Component field expansion of $(1,1)$ supersymmetric Polyakov action

I am working on the renormalizibility of two-dimensional nonlinear sigma models in string theory and particularly the $(1,1)$ supersymmetric extension of it. The following is based on the review by C. ...
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Background field expansion of supersymmetric string action

For a reasearch project I am studying the paper by L. Alvarez-Gaumé, D. Freedman and S. Mukhi called "The Background Field Method and the UV Structure of the Supersymmetric Nonlinear $\sigma$ ...
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F-theory questions on MSSM vs. SM compatibility and on de Sitter vacua

Having read https://arxiv.org/abs/2112.03947, https://arxiv.org/abs/1903.00009 and https://arxiv.org/abs/1903.00009, I noted the use of MSSM (Minimal Supersymmetric Standard Model) as if equivalent to ...
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Why use a spacetime indices when introducing supersymmetry for a point particle

In chapter $7$ of introduction to AdS/CFT correspondence Nastase states following: ... we generalize the first order action for the particle. The generalisation is done by introducing objects $\theta^...
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Is there superconformal group? (Exponentiating the superconformal algebra)

I (only superficially) know that not every Lie algebra can be exponentiated to give a Lie group. I also have only heard about the superconformal algebras, and not the superconformal groups. This is in ...
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Does $\mathcal{N}=1$ SCFTs have geometric constructions?

There are class S theories which are 4d $\mathcal{N}=2$ SCFTs by compactifying 6d $\mathcal{N}=(2,0)$ SCFT on a Riemann surface. Does similar geometric constructions exist for 4d $\mathcal{N}=1$ SCFTs?...
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Is there a non-lagrangian theory without conformal symmetry?

I have been reading about the questions and answers in (Does a non-lagrangian field theory have a stress-energy tensor?) and links in thereof. My question is the following. Are there non-Lagrangian ...
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Where are the multi-instantons in Supersymmetric QM?

Instantons can be used to find non perturbative corrections to ground state energies. However, the way in which they are used seems to me to be very different between the two common toy models of the ...
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What is Minahan-Nemeschansky’s theory?

Page 190 of ${\cal N}=2$ Supersymmetric Dynamics for Pedestrians Yuji Tachikawa book is saying; "Generalizing this to the E8 symmetry is by now rather straightforward. We perform the duality as ...
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Can local supersymmetry be characterized entirely in terms of observables?

Global symmetries can be defined through their effect on observables. In contrast, quantum theories are often constructed with the help of symmetries that leave observables invariant, like the ...
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One-dimensional Hamiltonian in SUSY Quantum Mechanics

I've seen in many places, in "Supersymmetry and Quantum Mechanics" of F. Cooper for example, that the hamiltonian in one dimension is defined: $$\hat H_1=\hat A^\dagger\hat A=-\frac{\hbar^2}{...
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Amount of SUSY preseved by branes

Consider 10d superstring theory, a D5 brane extended in the 012789 directions, and an NS5 brane extended in the 012345 directions. I have read that this configuration preserves 1/4 of the ...
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Confusion about Generating Functionals in AdS/CFT

I have a question regarding an equation in the book "Gauge/Gravity Duality" by Martin Ammon and Johanna Erdmenger which however can also be found in other AdS/CFT books or lecture notes. The ...
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Dimensional Reduction and Supersymmetry

I am working my way through "Basic Concepts of String Theory", by Blumenhagen, Lüst and Theisen. Currently I am working on the compactifications of string theories on Calabi-Yau manifolds. ...
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Is the seesaw mechanism for neutrino mass generation a supersymmetric model?

Since it introduces a right handed neutrino with greater mass i was wondering if this was a susy model? Or if not, how does it differ?
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3d supersymmetric theory

I just started studying supersymmetry and for a project I need to understand the vector multiplet field content of a 3d ${\cal N}=4$ theory in terms of 3d ${\cal N}=2$ multiplets. I tried approaching ...
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Two-twistors formulation vs twistors formulation

I have seen in some research work that the classic formulation using twistors (introduced by Penrose) is replaced with a formulation that considers two-twistors. For example the linking article says ...
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How do I draw the correct Feynman diagrammes of a Lagrangian for a given process?

Is there any method to somewhat rigorously determine the relevant Feynman diagrammes (no loops, $e^2$ approximation)? I don't by doing the full calculation of course. For example, I have the following ...
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Hierarchy Problem and SUSY: Quantum Loop Corrections

One of the reasons SUSY was developed in the 1970s is to solve the mass hierarchy problem with the Higgs, according to which the mass of the Higgs is "unnatural" (cf. https://arxiv.org/abs/...
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Is there a physical interpretation of Poincaré duality?

Is there a known interpretation of Poincaré duality in terms of a physical equivalence between (maybe topological) sectors of different (probably susy) quantum field theories?
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Chiral constraint on superfield

In SUSY to select the required supermultiplet from the entire set of fields in the general superfield we must impose the follow constraint $\bar{D}_{\dot{\alpha}}\Phi=0$ And a superfield subject to ...
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In context of MSSM, what is stop mixing?

In context of MSSM, what is stop mixing and stop mixing parameter?
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Can AdS/CFT still give bulk locality on small scales if the CFT has a nontrivial phase diagram?

The AdS/CFT correspondence is a well-supported conjecture about the equivalence between an ordinary conformal field theory (CFT) and a theory of quantum gravity in asymptotically anti-de Sitter (AdS) ...
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Number of unbroken supersymmetries in compactifications

In type II compactifications, we take a 10/11-d spinor $\epsilon$ to decompose into internal $\eta$ and external $\zeta$ pieces, $$\epsilon^1=\zeta^1\otimes\eta^1\ \ (+c.c.)$$ $$\epsilon^2=\zeta^2\...
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