Questions tagged [supersymmetry]

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

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Spinless particle in external and constant magnetic field

I'm trying to reproduce some calculations of a paper that consist in find the energy spectrum of a spin-less particle in a external and constant magnetic field, $B$, pointed in $z$ direction. I have ...
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Mass terms in the SUSY gauged linear sigma model

Okay, I have a very basic question about the SUSY gauged linear sigma model which is driving me crazy. I am following Chapter $15$ of Mirror Symmetry by Hori et al. I am considering the SUSY gauged ...
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Why aren't zero energy states paired in supersymmetry?

In a general supersymmetric theory, given a supercharge $Q$ and Hamiltonian $H$, one generally has $$[Q,H]=0$$ One can then say that given an energy eigenstate $|E\rangle$ with energy $E\ne 0$, then $$...
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Reference request for computing gluon scattering amplitudes in $\mathcal{N} = 4$ SYM in the planar limit

Could someone please provide me some reference(s), preferably that I can find online for free (arXiv for example or other), which would explain in some detail how to calculate gluon scattering ...
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SUSY Kinetic and $W$ potential terms: RG flow — free or interacting

In this Seiberg's SUSY lecture, the professor said that the following theory with Kinetic and $W$ potential terms: $$ K=|\phi|^2 $$ $$ W=m\phi^2+g \phi^3 $$ "It is not a valid theory in $4d$, ...
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Critical dimension of ${\cal N}=2$ strings

In "A tour through ${\cal N}=2$ strings" by Neil Marcus (https://arxiv.org/abs/hep-th/9211059) the following problem - among others - is noted: The critical dimension of the ${\cal N}=2$ ...
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R-symmetry constants in $\mathcal{N}=4$ SYM in Yukawa terms

The expression for $\mathcal{N}=4$ SYM in the Lorentz covariant form involves structure constants of $SU(4)$ R-symmetry group in the Yukawa terms (formula 3.1 from here https://arxiv.org/abs/hep-th/...
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Why is supersymmetry limited by $\frac{N}{4}$? [closed]

So in many people notes Bertolini's for example on page 9 it is stated that the limit of $N$ for SUSY is bound by $\frac{N}{4}$ in 4D. I understand that elementary particles can't have spin higher ...
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Forgotten term in the covariant form of $\mathcal{N}=4$ supersymmetric self-dual Yang-Mills theory?

For $\mathcal{N}=4$ supersymmetric self-dual Yang-Mills theory, the lightcone formulation reads: $$ \int d^{4} x \ d^{4} \theta \left( \frac{1}{2} V \Box V + \frac{1}{3} V [\partial_{+} V, \partial_{\...
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Beta function of Seiberg-Witten

In Seiberg and Witten's seminal paper, a key role is played by the monodromy of $\tau$ around infinity. This monodromy can be computed in the weakly coupled regime, and it is given by the one-loop ...
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Relation between the on-shell superspace and lightcone superspace

There is an on-shell superspace (introduced by V.Nair) for $\mathcal{N} = 4$. It is introduced in the section 4.3 in this paper https://arxiv.org/abs/1308.1697 , for instance. Four Grassmann variables ...
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Dimensionality of Grassmann numbers

I have noticed in a few texts ( Introduction to Supersymmetry by Harald J. W. Muller-Kirsten, Armin Wiedemann for instance) state that Grassmann variables that are used in superfields have dimension $\...
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Supersymmetry with two independent supercharges, $\mathcal N=4$, or $\mathcal N=(2,2)$, and physical significance?

My question is about a specific example of supersymmetry in quantum mechanics. I am not an expert on SUSY, and I would like to have some insights on this. Imagine you have a non-Hermitian supercharge $...
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$\mathcal{N}=1$ SUSY gauge theories in 2D?

The following introduction explains what I mean by $\mathcal{N}=1$ (often also called (1,1)) supersymmetry in 2D. We can define a superfield $$\Phi(x,\theta)=\phi(x)+\bar{\theta}\psi +\frac{1}{2}\bar{\...
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Lorentz Transformation of Supercharges in $d=1+1$

I am currently learning $\mathcal{N}=(2,2)$ SUSY and have come upon another probably silly issue. I am following chapter $12$ of Mirror Symmetry by Hori et. al. and am currently trying to derive the ...
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Has the ${\cal N}=1$ Minimal SUSY standard model been ruled out by the nature?

Question: Has the ${\cal N}=1$ Minimal SUSY standard model (MSSM) been ruled out by the nature? What are the natural constraints that ruled out such ${\cal N}=1$ MSSM? In particular, the ${\cal N}=1$...
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How do I prove that the product of chiral superfields is itself a chiral superfield?

I am currently learning about $\mathcal{N}=(2,2)$ supersymmetry and have come up against what is probably a really silly question. The $\mathcal{}N=(2,2)$ superspace consists of bosonic coordinates $x^...
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Derivation of anti-commutation relations of massive supermultiplet generators [closed]

In almost all intro to supersymmetry notes the commutation relations are given between the generators and their conjugates however, I can not find any proofs of them anywhere and am struggling to ...
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Can Montonen-Olive duality be used for studying $\mathcal{N}=4$ SYM at strong coupling? If not, why not?

It's all in the title. To be more complete, the following is stated in the preamble of the Wikipedia article about S-duality: One of the earliest known examples of S-duality in quantum field theory ...
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Terminology about chiral supermultiplet and vector supermultiplet

I have an issue with the terminology about chiral supermultiplet and vector supermultiplet. In the Pierre Ramond's Journeys Beyond The Standard Model p.286, he used the phrase chiral vector multiplet ...
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Bosonization of $\beta \gamma$ system

I am studying the bosonization of the $\beta \gamma$ ghost system, also called as the symplectic boson (See for example, section 2.3 of this paper. These have OPE, \begin{equation} \beta(z) \gamma(w) \...
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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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Rewriting an expression into a manifestly supersymmetric form

In $\mathcal{N}=2$ supersymmetry, one can define the following superderivatives \begin{equation} D_{\theta}=\partial_{\theta}+\frac{1}{2}\bar{\theta}\partial_{u}, \hspace{4mm} D_{\bar{\theta}}=\...
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Possible errata in Weinberg volume 3 (SUSY calculation)

I am wondering if I have spotted an errata in Weinberg volume 3, equation 26.1.3. Here is my derivation. Let $Q_b$ be supersymmetric symmetry generators and $\zeta_a$ spinor fields given in terms of ...
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Which non-homogeneous scalar manifolds are possible in supergravity?

The scalar fields in various supergravity theories are restricted (by supersymmetry) to span the target (scalar) manifolds of a certain class (e.g. Hodge-Kahler, quaternion-Kahler etc.), depending on ...
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Why does putting field theory on $S^4$ deform the scalar kinetic term?

I was reading the famous localization paper by Pestun, where he proves, among other things, that $\mathcal{N}=4$ super Yang-Mills (SYM) on $S^4$ localizes to a Gaussian matrix model. However, I was ...
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Gauging R-Symmetry

I know that if one gauges the supersymmetry group, you get supergravity. You can then further gauge the R-symmetry and these are the so-called gauged supergravities. But I don't think I've seen anyone ...
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Why are explicit mass terms allowed for sfermions like higgsinos and gauginos in the MSSM Lagranian if explicit fermionic mass terms are prohibited?

In Martin's SUSY Primer, he claims: For the higgsinos and gauginos, [the ability to have a mass term] follows from the fact that they are fermions in a real representation of the gauge group. As I ...
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How to decompose the spinor kinetic term of $D=10$ SYM in terms of lower dimensional parts?

The kinetic term for the spinors in $D=10$ SYM is $\lambda \gamma^\mu \partial_\mu \lambda$, where $\lambda$ is a 16 component Majorana-Weyl spinor and $\gamma^\mu$ is a 16 by 16 matrix satisfying $\{\...
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Question for ${\cal N}=1$ supersymmetry representations

Please see this lecture note: https://arxiv.org/abs/1011.1491. In section "2.2.5 Massless supermultiplet" the author defines a Casimir and says it is zero. How can we confirm it? We take the ...
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Electron as Superpartner of Higgs!

Can we identify Higgs as a superpartner of the electron in a massless case? We know, superpartners have the same mass so of course, we can't and one argument we can make there are two Higgs doublets ...
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BRST invariant vertex operator

I'm trying to compute the commutator $\left[Q_{BRST}(z), V^{-1/2}_{v}(w)\right]$, where $V^{-1/2}_{v}(w)$ is the vertex operator corresponding to a massive fermion state. The vertex reads $$ V_{v}^{-\...
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Notation problem in Yukawa-like interaction - from SUSY?

I am struggling to understand the meaning of a term in a Lagrangian of a paper I am reading. I think it is a notation issue. The term is: $$\lambda_e \bar{\nu}_L^c l_L \Sigma^{\dagger}_e$$ where $\...
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Periodic boundary conditions in Partition Function (Supersymmetry of stochastic dynamics)

In the context of supersymmetric theory of stochastic dynamics one introduces a partition function for a field satisfying a Langevin equation, starting from the partition function of the noise. As ...
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Renormalization of the coupling constant in $\mathcal{N}=1$ SYM

I have been watching the lecture https://youtu.be/lrikIt9MXpQ from the school LACES 2020 by INFN. The $\mathcal{N}=1$ SYM is investigated, with the action: $$ \mathcal{L} = \frac{1}{32\pi} \mathrm{Im} ...
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Invariant of supersymmetry?

Given two vectors in 3D superspace $(x_1^\mu,\theta_1^\alpha,\overline{\theta}_1^\alpha)$ and $(x_2^\mu,\theta_2^\alpha,\overline{\theta}_2^\alpha)$ I am trying to find a polynomial invariant under ...
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Holomorphic anomaly at genus 1

Partition function on torus can be defined using a generalized Witten like index as given below: $$F_1=\int_\mathbb{T}\frac{d^2\tau}{\tau_2} Tr(-1)^F F_LF_R \;q^{L_0} \bar{q}^{\bar{L_0}},$$ where $\...
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Polchinski “String theory” (B.2.8)

The $\mathcal N = 1$ algebra \begin{equation} \{Q_\alpha,\overline Q_\beta\} = -2P_\mu\Gamma^\mu_{\alpha\beta} \end{equation} is in a frame where $k_1 = k_0$ \begin{equation} \{Q_\alpha, Q_\beta^\...
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Textbook reference: Superstring Theory [closed]

I have almost finished reading the basics of Bosonic String Theory from Becker, Becker and Schwartz as well as Tong's notes. What is the best book to start reading about Superstring theory (something ...
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Chemical potentials for D-brane bound states

This question is about a mathematical subtlety arising in the computation of the partition function of a supersymmetric ensemble of some lower dimensional $D$-branes attached to a stack of higher ...
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Commutation relations of derivatives of fermionic fields from the commutation relations of the original fields

I have a general question regarding such type of calculations, but let me start with a concrete question. Consider the $bc$- free fermion CFT so that $b(z)$ and $c(z)$ are free fermions with OPE, $$b(...
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Is there a systematic way to construct a SUSY theory?

For the sake of simplicity, I am considering a 0+0d scalar field theory with multiple bosonic and fermionic fields/variables. The fields are coupled together up to a certain order (say 4) with ...
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Show that a system of intersecting $D4$-$D6$ branes is supersymmetric

The paper "Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions" asserts (first paragraph, page 12,section 2.4) that a system of $N$ $D4$-branes intersecting with $k$ $D6$ ...
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On Goldstone fermions / goldstino: SUSY breaking

There are statements about Goldstone fermions, or goldstino, seem confusing to me. (1) Goldstone boson requires a continuous symmetry spontaneously broken. Does Goldstone fermion imply continuous SUSY ...
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Precise zero energy bound for supersymmetry

Usually we can shift the energy $E$ by any amount $\delta$ to redefine the lowest energy as $$ E + \delta. $$ However, in supersymmetry, there is a precise $E=0$ must be true, so that the supercharge $...
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Supersymmetry infinitesimal variation

In Wess & Bagger, chapter 3, the infinitesimal supersymmetric transformation is defined as: $$ \delta_\xi \psi = i\sqrt{2} \ \sigma^m \bar{\xi}\partial_m A + \sqrt{2} \ \xi F$$ and $$\delta_\xi A =...
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Supersymmetry non-breaking $\iff$ no “Goldstone fermion”?

In Supersymmetry and Morse Theory (1982) by E Witten, Concern whether the supersymmetry is broken by checking whether $$ Q | 0 \rangle=0 $$ exists or not --- Witten said: SUSY breaking: A solution ...
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STU supergravity

Tghere are a lot of different papers about STU supergravity, for example see this. As I understand, STU supergravity is N = 2 supergravity coupled to three vector multiplets. Could someone explain, ...
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Non-extended and extended SUSY

What are the distinctions between Non-extended SUSY and Extended SUSY? (Is that just a non-extended SUSY has $\mathcal{N}=1$ while the extended SUSY has $\mathcal{N}>1$ ? Then there is no ...
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Physical interpretation of spinor parameter $\epsilon$ in supersymmetry

Studying supersymmetry, I came across the introduction of the idea of SUSY field variations involving spinor parameters $\epsilon_{\alpha}$ under which actions must be invariant. This spinor parameter ...

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