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Questions tagged [supersymmetry]

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

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How to get the mass squared for the Green-Schwarz string?

Im following the GSW book. Specifically equations (5.2.39), (5.2.40) $$H=\frac{1}{2p^-}((p^i)^2+2N)$$ $$N=\sum_{m=1}^\infty(\alpha_{-m}^i\alpha_m^i+mS_{-m}^aS_{m}^a)$$ are not clear for me. I know, ...
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Silly Question about Supersymmetric Gauge Theory

In $\mathcal{N}=1$ super electrodynamics, one has the following vector superfield $$V(x,\theta,\bar{\theta})=\bar{\theta}\bar{\sigma}^{\mu}\theta v_{\mu}(x)+\bar{\theta}^{2}\theta\lambda+\theta^{2}\...
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Understanding the idea behind the super-Poincaré algebra

On the Super-poincaré algebra wiki page (https://en.m.wikipedia.org/wiki/Super-Poincaré_algebra), it says: "If Minkowski space-time belongs to the adjoint representation, then can Poincaré symmetry ...
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Is Lorentz symmetry broken if SUSY is broken?

I have seemingly convinced myself that the entire Poincare group is spontaneously broken if one of the supersymmetric charges is spontaneously broken. We know that if one of the supersymmetric ...
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A Question About Vector Superfield

My reference is section 5.2 of BUSSTEPP Lectures on Supersymmetry, page 46. A Vector superfield $V$ is a scalar superfield which satisfies the reality condition $$V=\overline{V},$$ where the bar ...
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What is the relation between a $D_2$-brane and an $M2$-brane?

I am only familiar with the concept of a $D_2$-brane from a first course in String theory. I would like to learn, at least on a conceptual level, what an $M2$-brane is and what is its relation to the $...
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Why should fermions vanish for a solution of a supergravity theory that preserves supersymmetry?

On p.249 of Freedman and Van Proeyen's Supergravity, the following is stated: "Given the action of a supergravity theory, it is generally useful to search for solutions of the classical equations ...
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Cubic Power of Supercovariant Derivative

Let $\bar{D}_{\dot{\alpha}}=\bar{\partial}_{\dot{\alpha}}-i(\bar{\sigma}^{\mu})_{\dot{\alpha}\beta}\theta^{\theta}\partial_{\mu}$ be the supercovariant derivative. How to prove the following identity? ...
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A Question about Supercovariant Derivative

Let $\Phi(x,\theta,\bar{\theta})$ be a complex superfield. Let $K(\Phi,\bar{\Phi})$ be a function of $\Phi$ and $\bar{\Phi}$. How to prove the following identity? $$\int d^{4}x\int d^{2}\theta d^{2}\...
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Sources to learn about Killing spinors

What are some good sources to learn about Killing spinors from? I am currently learning about Killing vectors and how they are the generators of a Lie algebra that corresponds to the isometry group ...
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The logic behind a specific step of SUSY variation

I'm following Neil Lambert's Supersymmetry notes, and there's a step in equation 5.67 which has me stumped. He says he uses the fact that "$C\gamma_\mu$ is symmetric". I don't see how that helps, and ...
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Trying to prove the Wess Zumino invariance under a SUSY transformation

I have the Lagrangian density $$L=-\partial_\mu \phi^\star \partial^\mu \phi - \bar{\chi}_R \gamma^\mu \partial_\mu \chi_L - \bar{\chi}_L\gamma^\mu\partial_\mu \chi_R.$$ where $\epsilon$ is the ...
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Representations of the SUSY algebra

I am currently reading Wess & Bagger, and have trouble with a statement they make about representations. If we wish to study massive, one-particle representations of the SUSY algebra, we boost to ...
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What's a good book on supersymmetric quantum mechanics for an undergraduate?

I'm a third-year undergraduate student, and halfway through a seminar on quantum mechanics, my second course in the subject. This semester, we've used Townsend's A Modern Approach to Quantum Mechanics,...
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Question about Pauli Matrices

I found the following identities about Pauli matrices from the lecture notes of Supersymmetry. $$((\sigma^{\mu})^{\alpha\dot{\alpha}})^{\ast}=(\bar{\sigma}^{\mu})^{\dot{\alpha}\alpha}$$ $$((\sigma_{\...
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Is the supercurrent gauge invariant?

If we consider ${\cal N}=1$ renormalizeable chiral gauge theories, specifically discussed in section 27.4 of Weinberg's Quantum Theory of Fields, Supersymmetry book, should the supercurrent be gauge ...
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I want to know the conformal weights of spinors in 2D

I want to know the conformal weights(or dimensions) of left/right-moving fermions in 2D, ${\cal N}=(2,2)$ superconformal theory. More specifically, what is the left/right-moving conformal dimension ($...
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Showing that the $\mathcal{N=2}$ SUSY Effective Action is Duality-Invariant

The effective action of the $\mathcal{N}=2$ supersymmetric $SU(2)$ gauge theory contains the following term; $$Im\int d^{4}xd^{2}\theta d^{2}\bar{\theta}\Phi^{\dagger}\mathcal{F}'(\Phi)$$ Where $\...
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Describe supersymmetry to a non-physicist in few sentences

Can someone help me describe the idea of supersymmetry in a few sentences, to a broad scientific audience? That is, a science or engineering graduate student who hasn't studied much theoretical ...
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What is the high-energy/superstring analogue of wave function?

Chapter 12 of Beckers' book about superstrings and m-theory lists several deep dualities between low energy gauge theories and high energy superstring theories. I am only at the Chapter 2, that is why ...
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singularity blow up in supersymmetric theories

I have been doing some reading on algebraic geometry, in particular singularity resolutions. All the examples I am familiar with in physics correspond to singularities of the extra dimensions (e.g. ...
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My Struggle with Fierz Identity

I am following BUSSTEPP Lectures on Supersymmetry to learn SUSY. The Lagrangian of a interacting Wess-Zumino model in 4D is given by $$\mathcal{L}=-\frac{1}{2}(\partial_{\mu}S)(\partial^{\mu}S)-\...
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A Naive Question about SUSY Variation

I am following BUSSTEPP Lectures on Supersymmetry to learn supersymmetry. My simple question is the following. My Lagrangian for the Wess-Zumino model in $4D$ is $$\mathcal{L}=-\frac{1}{2}(\...
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A few questions about spinors and gamma matrices

I am following BUSSTEPP Lectures on Supersymmetry and trying to show that the Wess-Zumino action is invariant under SUSY transformations. I encountered the following questions about spinors and gamma ...
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‘Supersymmetrizing’ an arbitrary quantum-mechanical potential

To my understanding, it is not possible to $``\text{supersymmetrize}"$ an arbitrary quantum-mechanical system unless one knows how to represent the corresponding Hamiltonian in the form $$ H = A^\...
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Why does a SUSY Lagrangian only contain $F$ and $D$-terms?

I'm reading a book on AdS/CFT by Ammon and Erdmenger and chapter 3 covers supersymmetry. This isn't my first look at SUSY but it's my first in depth look to really try to understand it, and when they ...
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What is the difference between supersymmetry and MSSM?

What is the difference between supersymmetry and MSSM? Please explain in a simple language i am just a beginner of supersymmetry
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Can supersymmetry be disproved? [duplicate]

Recently there are a lot of news about the plans to build the FCC accelerator, with many claims of possibilities to find new particles, for example like those suggested by theories of supersymmetry. ...
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Resources on Gubeser-Klebanov-Polyakov (GKP) strings and N=4 Super-Yang Mills dual description

*I have learned recently that the Gubeser-Klebanov-Polyakov string / folded string in AdS3 (if I recall correctly, and I assume with some additional virasoro constraints, etc) is dual to large-spin ...
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Are there supersymmetry algebras with higher spinor representations?

The super-Poincare algebra contains supersymmetry generators $Q^I$ which satisfy fermionic anticommutation relations. By the higher-dimensional analogue of the spin-statistics theorem, they must ...
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What are the main physical consequences of supergravity?

String theory in some limit becomes supergravity. This is the super generalisation of gravity where instead of taking the Poincare symmetry as the local symmetry of spacetime we take the super-...
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Commutation relations of symmetry generators in SUSY

It is well known that the generators $$ Q_\alpha = \frac{\partial}{\partial \theta^\alpha} - i \sigma^\mu_{\alpha \dot \beta} \bar{\theta}^\dot{\beta} \partial_\mu $$ and $$ \bar{Q}_\dot{\alpha} = -\...
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Checking modularity-like transformation property

Assume $M$ is a 4 manifold. Let $Z_v$ be partition function of fixed magnetic flux $v$ with all instanton configuration summed over where $v\in H^2(M,Z/nZ)$. $\tau$ denotes complex parameter on upper ...
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Where can I find the detailed calculation for the mass of the lights Higgs boson in MSSM?

can somebody mention where the mass of the lights Higgs boson in MSSM (minimal supersymmetric standard model) is discussed? I need a detailed and thorough explanation of the subject mater. I ...
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What does $\mathcal{N}$ refer to in Gauge theories?

Context: I am a second-year (undergraduate) physics major applying for a summer research position. The investigator is working on Quiver Gauge Theories and in response to my inquiry email he told me ...
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Spinning Particles in Background Gauge Fields

A simple model for a spinning particle is $$L=m\int dt\left(\dot{x}^{2}-\frac{i}{2}\psi\dot{\psi}\right)$$ with SUSY algebra $\delta x=-i\epsilon\psi$ and $\delta\psi=-\epsilon\dot{x}$, where $\...
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SUSY variation Wess-Zumino

I'm following John Terning book on Supersymmetry and in particular I'm trying to check the susy variations of the Wess-Zumino model given by $\mathcal{L}_s = \partial^\mu \phi^* \partial_\mu \psi \,...
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Differentiating D3 brane worldvolume theories with NS5 brane and NS5 antibrane boundary conditions

In 'Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory', Gaiotto and Witten derive boundary conditions for the worldvolume theory of the D3 brane. In particular the boundary conditions (...
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Intuition for the supertrace identity in supersymmetry

In pretty much every introductory book/lecture notes I've come across, one finds the expression for the mass matrices for scalars, fermions and vector bosons for a generic Lagrangian, and simply ...
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Transformation algebra of supersymmetry transformation

Given supersmmetry transformation: $$δX^\mu = i\barξψ^\mu.δψ^\mu = ξγ^a(∂_aX^\mu-\frac i2\barχ_a ψ^\mu). δχ_a = 2 D_aξ.$$ How to calculate the transformation algebra of $X^\mu$ and $\psi^\mu$? ...
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Supersymmetry and reparametrization invariance of superstring action

Section $4.3.5$ Superstring action and its symmetries, Page$229$ Superstring theory by Green, Schwarz and Witten. $S_1=-\frac1{2π} ∫d^2σ\ eh^{αβ}∂_αX^μ∂_βX_μ.\quad S_2=\frac i{2π}∫d^2σ\ e\barψ^μρ^α∇...
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Constrained Hamiltonian systems: spin 1/2 particle

I am trying to apply the Constrained Hamiltonian Systems theory on relativistic particles. For what concerns the scalar particle there is no issue. Indeed, I have the action \begin{equation} S=-m\int ...
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61 views

SUSY vacuum has 0 energy?

This is related to Modern Supersymmetry: Dynamics and Duality by Terning. Consider $N=1$ SUSY. $\{Q_a,\bar{Q}_{\dot{a}}\}=2\sigma_{a\dot{a}}^\mu P_\mu$. Sum over $a=\dot{a}=1,2$ and this yields $4P^...
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A few basic questions on SUSY algebra

Consider SUSY generator taking the form {$Q_a^A,Q_{\dot{b}B}$}$=\delta_{a\dot{b}}\delta^A_B$ and {$Q_a^A,Q^B_b$}={$\bar{Q}_{\dot{a}A},\bar{Q}_{\dot{b} B}$}=0 where $a,b$ label spinor index and $A,B$ ...
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${\cal N} = 1$ SUSY Non-renormalization theorem

In Ref. 1, on Page 53, the ${\cal N} = 1$ SUSY non-renormalization theorem is derived. One first specifies the symmetries of the general ${\cal N} = 1$ SUSY action in the superspace formalism, and ...
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Symmetries on String theory

Recently I was watching and reading about String theory, M-theory and the supersymmetry, when I remembered one question that I had while reading 'The Elegant Universe' by Brian Greene that is: why do ...
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Gauge fixing while preserving supersymmetry

In supersymmetric gauge theories, the vector potential is a part of a vector supermultiplet which is represented by a real superfield $V$. Expanded out in components, the Lagrangian for such a field ...
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Supercharge transformation rules

Consider ${\cal N}=2$ supersymmetry with $SU(2)$ global symmetry group. Then both supercharges $Q_{ai},\bar{Q}_{\dot{a}\dot{j}}$ transform by 2 dimensional representation of $SU(2)$. Denote $SU(2)_I$ ...
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Partition function computation on a Riemannian Manifold

This discussion comes from Chapter 10, Mirror Symmetry. I am given a Riemannian manifold $M$, and a classical (Euclidean) theory: $$(1)\quad S_E={\int}_0^\beta d\tau\space\Bigl(\frac{1}{2}g_{ij}{\dot{...
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Vandermonde determinant factor in supersymmetric gauge localisation computation

I am trying to learn supersymmetric localisation computation in which the path integral of a supersymmetric gauge theory (placed on a sphere) can be localised exactly to a BPS configuration ...