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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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What does a supercharge physically conserve? [duplicate]

What is actually being conserved? I've calculated it for the Wess-Zumino model but I still have no idea what is actually being conserved due to Noether's Theorem. There is already a similar question, ...
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Supersymmetry Generator Definition for ${\cal N }= 1$

I am studying SYM $\mathcal{N}$ = 1 in D = 10, and using the bimodular representations for the 32x32 gamma matrices $\Gamma^a$. This means that I work with the off-diagonal 16x16 matrices, which I ...
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No supersymmetric particles have been found in the LHC. Isn't this proof that Supersymmetry doesn't exist? [duplicate]

The LHC can reach energies from $7(TeV)$ to $13(TeV)$ (see here) and the question of which this is supposed a duplicate. Which I think it isn't, because in that question (which has been asked already ...
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Spontaneous breaking of supersymmetry

I am a beginner in SUSY Quantum mechanics. I had read that the symmetry is spontaneously broken if $A \left|\psi \right>_n^{(1)}\neq 0 $ and symmetric if $A \left|\psi \right>_n^{(1)}= 0. $ But ...
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Meaning of mass-deformation in string theory and quantum field theories

I was reading some papers in the ABJM theory. I keep reading the term mass deformation but am not sure what it really means. I think the papers assume the reader is familiar with the term. Example ...
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Hamiltonian and Supercharges

Mirror Symmetry p.188 Eq. 10.109 states that $$H \left\vert \alpha\right> = 0 \Longleftrightarrow Q \left\vert\alpha\right> = \overline{Q} \left\vert\alpha\right> =0. \tag{10.109}$$ I dont ...
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Anticommutativity of an anticommutator of supercharges

In this paper, equation 38 gives the ${\cal N}=2$ Super-Poincare (extended with the central extension $\mathcal{Z}$). The anticommutation relation of the two different supercharges is given as: $$\{Q^...
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Lefschetz and Witten indices$.$

I couldn't help but notice a formal similarity between the Lefschetz index $$ \mathrm{ind}(f)=\sum_k (-1)^k\operatorname{tr}(f_*|H_k) $$ and the Witten index $$ Z=\operatorname{tr}((-1)^Fe^{-\beta H}) ...
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SUSY Breaking in the Vacuum

Under what conditions is supersymmetry preserved in the vacuum state? In particular, suppose I have some super potential $W(x)$ which does not permit normalizable ground-state wave functions (such as $...
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A question on supersymmetry variation of the Wilson loop in $\mathcal{N}=4$ SYM

The Wilson loop in $\mathcal{N}=4$ SYM is $$W=\frac{1}{N}tr P \exp \int ds (i A_\mu(x) \dot{x}^\mu+\Phi_i(x)\theta^i|\dot{x}|).\tag{2.3}$$ In order to check whether this operator is supersymmetric I ...
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Localization Principle (SUSY)

Mirror Symmetry p.200/201 Last section p.200/first p.201 It says, that the localization principle would not work if one would not impose periodic boundary conditions for the fermion integration, ...
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Why is supersymmetry a continuous symmetry?

Supersymmetry feels like a discrete symmetry to me, since the fermions are turning into bosons, and vice versa. I understand there is an infinitesimal parameter involved in the transformations, but I ...
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Vanishing correlation function

Mirror Symmetry p. 206, Eq. 10.192. I have an operator $\mathcal{O}$ that commutes with my supercharge $\overline{Q}_+ $, $\left[\overline{Q}_+, \mathcal{O} \right]=0$. Why does the correlation ...
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Wavefunction Renormalization in Wess-Zumino Model

In Modern Supersymmetry: Dynamics and Duality, on page 134 and 135 in section 8.2, the authors studied the wavefunction renormalization of the Wess-Zumino model. The kinetic terms are given by $$\...
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Supersymmetry Perturbation Theory

Source:Mirror Symmetry p.198 I have the Hamiltonian $$H = \lambda\bigg( \frac{1}{2} \tilde{p} + \frac{1}{2}h''(x_i)^2(\tilde{x}-\tilde{x_i})^2 + \frac{1}{2}h''(x_i)[\overline{\psi}, \psi] \bigg) + \...
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Dark matter and supersymmetric particles

Is there a possibility to consider supersymmetric particles of fermions and bosons as the unknown dark matter?
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Book with explanation of Kazama-Suzuki models

The book "Introduction to Conformal Field Theory" by Blumenhagen and Plauschinn (BP) covers coset construction and minimal models, but it stops there. The original papers by Kazama and Suzuki seem to ...
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Witten Index of Riemannian Manifold

Consider a system on a Riemannian manifold with the Lagrangian $$L = \frac{1}{2}g_{IJ} \dot{\phi}^I \dot{\phi}^J + \frac{i}{2}g_{IJ}(\overline{\psi}^I D_t \psi^J - D_t \overline{\psi}^I \psi^J) - \...
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Vanishing partition function [duplicate]

I am currently stuck with the following partition function Let the action be $$S(X, \psi^1, \psi^2) = \frac{1}{2} (\partial h)^2 - \partial^2h\psi^1 \psi^2 ,$$ where $h$ is a real function of the ...
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Grassmann-even action

I am currently studying supersymmetric quantum mechanics with the help of the book Mirror Symmetry by Kentaro Hori (and others). On page 155 where they introduce Grassmann variables they say that the ...
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What is a global limit in gauged supergravity?

Does anyone know what a global limit (rigid limit), where the gauge coupling constant is zero, in gauged supergravity is?
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$R$-Symmetry of gauge field

Suppose $V$ is a superfield scalar under R-transformations. This means that under an R-transformation $V\mapsto V'$ where $V'(x,\theta,\bar{\theta})=V(x,e^{-iK}\theta,e^{iK}\bar{\theta})$. What is ...
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What is the physical meaning of a Supercharge?

What is actually being conserved? I've calculated it for the Wess-Zumino model but I still have no idea what is actually being conserved due to Noether's Theorem. There is already a similar question, ...
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0answers
32 views

What is an optical supermode?

What is an optical supermode? Is it related to a specific type of symmetry? Am studying a paper, Parity anomaly laser. D.A. Smirnova et al. Opt. Lett. 44, 1120 (2019), arXiv:1811.06300 that ...
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1answer
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Super GoldStone model and SuperHiggs theorem

I am currently studying SuperSymmetry and I have reached a problem which I have not found an answer to. I clearly understand how the Goldstone theorem works for the boson case (without any susy) ...
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Anti-Commutator of derivatives of Grassmann variables

How do I evaluate the anti-commutator of $\frac{\partial}{\partial\chi}$ and $\frac{\partial}{\partial\eta}$ when both $\chi$ and $\eta$ are Grassmann variables?
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A Question about Wess-Zumino Gauge in Non-Abelian Gauge Theory

I have a question about the Wess-Zumino gauge in non-Abelian supersymmetric gauge theory. I am following BUSSTEPP Lectures on Supersymmetry. The spinortial field strength is defined as $$W_{\alpha}(...
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Fermionic contribution to central charge in $\mathcal{N}=2$ Super Yang-Mills?

I am trying to replicate the calculation of the central charge for $\mathcal{N}=2$ Super Yang-Mills, by following Weinberg's textbook in section 27.9. He calculates it by finding how one supercurrent ...
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2answers
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Can gamma matrices be real in 6 dimensions?

I'm trying to find the really real representation of 6D gamma matrices. The problem is that "do they really exist?" If yes, then how am I supposed to construct them? Thank you!
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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. ...