Questions tagged [supersymmetry]

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

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How does chiral symmetry protect modes in optics?

I am reading a paper on the use of SUSY to create a robust lasing mode in optical cavities. In this paper, SUSY is used to create a super-hamiltonian of the form: $$ Q = \left ( \begin{matrix} 0 &...
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What would we have to find to prove supersymmetry correct?

What would we have to find to prove that supersymmetry is true?
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Picture Number Operator in String Theory

My question concerns the ghost picture charge/picture number operator in the RNS formalism of Superstring theory. In particular I refer to page 403 of "Basic Concepts of String Theory" by R. ...
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Dyon and monopole are mutually non-local objects?

Why dyon and monopole are mutually non-local objects? This statement from Matteo Bertolini: Lectures on Supersymmetry, section 12.3.3 and related to this question.
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Argyres-Douglas CFT

Adding of mass in supersymmetric gauge theories will affect structure of moduli space by creating new singular point (picture and some statements from Matteo Bertolini: Lectures on Supersymmetry): ...
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Hermitean conjugate of spinor product

Consider spinors $\psi_\alpha$ in the $(0,1/2)$ rep and $\bar{\psi}_{\dot{\alpha}}$ in the $(1/2,0)$ rep. I'm using notation from the following notes. All we will need is the totally antisymmetric 2x2 ...
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What is the difference between type IIA and type 0A string theory?

When people study string theory the most useful models are IIA and IIB. I'm not quite sure I understand what is the difference between 0A and IIA string theory. In the type 0 case we only have bosons ...
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Am I reading this Feynman diagram in $\mathcal{N}=4$ SYM right?

I would like to find the expression corresponding to the scalar-gluon sunset diagram in position space, for Euclidean $\mathcal{N}=4$ Super Yang-Mills theory. The diagram is the following: where the ...
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Scalar self-energy in $\mathcal{N}=4$ SYM in position space

In this paper (BMN Correlators and Operator Mixing in $\mathcal{N}=4$ Super Yang-Mills Theory, 2002), the authors give the following expression for the self-energy of the scalar propagator in $\...
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String Theory, SUSY, and the hierarchy problem

Can SUSY yet succeed for String Theory, given that it has failed to solve the hierarchy problem? I'm not looking for how ST could succeed without SUSY, but rather how and why SUSY could still be found ...
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Supersymmetric localisation of 2D super YM on $S^2$

I wanna to understand how to calculate partition function for pure abelian Yang-Mills theory. To do this, I need follow some usual step's (I follow Benini, Localization in supersymmetric field ...
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Applying SUSY operator to highest eigenvector. What happens?

A Hamiltonian $$ H_1 = A^\dagger A $$ and it's super-partner: $$ H_2=AA^\dagger $$ Follow the interwinning relationships $$ \psi^2_n \propto A\psi^1_{n+1} $$ $$ \psi^1_{n+1} \propto A^\dagger \psi^...
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Supersymmetry and Elko spinors

Now, very popular subject is Elko spinors. Is it possible to construct supersymmetric theory with Elko spinors as parameters of susy transformations?
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RNS string theory: supersymmetry in open and closed strings

After reading the chapter "Strings with world-sheet supersymmetry" in Becker, Becker, Schwarz book multiple times, I am still confused about the following things. 1) Open string doubt They prove ...
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Grassmann confusion

I am trying to calculate $$\mathcal{\bar{D}}_\dot{\alpha}y^\mu= \left(\bar{\partial_\dot{\alpha}}+i\theta^\alpha\sigma^\mu_{\alpha\dot{\alpha}}\partial_\mu\right)\left(x^\mu+i\theta^\beta\sigma^\mu_{\...
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Invariance of superstring action under super-Weyl transformation

Keeping with the notation on page 178 of the text "Basic concepts of string theory", in superstring theory, consider the action \begin{align} S=\frac{1}{8 \pi} \int d^2\sigma e \left(\frac{2}{\alpha} ...
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Prove that the superstring theory is invariant under supersymmetry

So, as in the title, I am looking for a proof that the superstring theory action (in Minkowski spacetime with conformal gauge): $$S=\int d^2\sigma \eta_{AB} (\eta^{ab} \partial_aX^A\partial_bX^B-i\...
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SUSY $\mathcal{N}=1$ algebra

Given the definitions $$ P_\mu= -i\partial_\mu $$ $$ Q_\alpha=-i(\partial_\alpha-(\sigma^\mu\bar{\theta})_\alpha\partial_\mu) $$ $$ \bar{Q_\dot{\alpha}}=+i(\bar{\partial}_\dot{\alpha}-({\theta}\sigma^...
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Superspace integrals

I understand the definition of the Grassmann Integral, which is as follows: $$ \int{d\theta}=0,\;\;\;\;\;\; \int{d\theta}\;\theta=1 \tag{4.17} $$ with $$\int{d\theta}=\frac{\partial}{\partial\theta}.\...
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$\mathcal{N} \ge 2$ Supersymmetry massive supermultiplets

In Bertolinis SUSY notes [https://people.sissa.it/~bertmat/susycourse.pdf] we have defined: $$ \{Q^I_\alpha,\bar{Q}_\dot{\beta}^J\}=2m\delta_{\alpha\dot{\beta}}\delta^{IJ}\tag{3.24} $$ $$ \{Q^I_\alpha,...
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SUSY sigma model in QM, bosonic sector?

The bosonic sigma model in ordinary QM (i.e. a 'free' particle trapped on a curved manifold $\mathcal{M}$), has a Hamiltonian which is just the negative Laplacian on $\mathcal{M}$. For any $\mathcal{...
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Showing the energy of states is positive in SUSY

When we consider the energy of any state in supersymmetry we calculate: $$ \langle\phi|\{Q^I_\alpha,\bar{Q}^I_{\dot{\alpha}}\}|\phi\rangle=2\sigma^\mu_{\alpha\dot{\alpha}}\langle\phi|P_\mu|\phi\rangle\...
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$\Delta {b_{L}}$, $\Delta {b_{Y}}$ and $\Delta {b_{C}}$ and unification of couplings

In any standard book on QFT, I understand how to find out the beta function for Standard Model and for Minimal Supersymmetric Standard Model, but i could not understand how this beta function changes ...
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Supersymmetry in de Sitter space

Is it possible to construct SUSY theories in de Sitter space? I know statement: dS superalgebras cannot be constructed unless one constructs actions with matter coupled with the wrong signs for ...
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What is the meaning of a Grassmann variable?

I don't seem to understand the concept of a Grassmann-variable. When studying superspaces and superfields I am told that the coordinates being used are $$(x^\mu, \theta_\alpha, \bar{\theta}_\alpha)$$ ...
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Are the momenta of the $1/2$-BPS operators in this $2$-point function on-shell?

I recently asked this question about the Fourier transform of a $2$-point function, and it lead me to another question. I am looking at $2$-pt functions of $1/2$-BPS operators in $\mathcal{N}=4$ SYM ...
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$SU(2)_R$ symmetry and mass term for hypermultiplet

I study N=2 supersymmetric dynamics for pedestrians by Yuji Tachikawa, and I don't understand how $SU(2)_R$ symmetry demands that $[\mu, \mu^\dagger] = 0$. I will be very appreciate for answers.
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Supercharge in $\mathcal{N}=1$ supersymmetric quantum mechanics and Noether's theorem

Consider the $0+1$ dimensional Lagrangian $$L=\frac{1}{2}\dot{X}^2(t)+i \psi(t) \dot{\psi}(t).\tag{1.24}$$ Essentially this the Lagrangian of a particle moving in one dimension, $X$, with an ...
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Behavior of derivative on Lorentz transformations of spinors

I'm currently working through Supersymmetry Demystified by Patrick Labelle and one passage in particular confuses me. Specifically, if $\eta$ and $\chi$ are right and left Weyl spinors respectively, ...
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Are the factors of SUSY factorization the conjugate transpose of each other?

I am trying to learn about SUSY by reading Freed Cooper, et al. I understand that a Hamiltonian with ground state energy equal to $0$ ($E_0=0$). $$ - \frac{\hbar^2}{2 m} \frac{d^2}{d x^2} \psi_0 +...
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String Landscape, De Sitter vacua and Broken Supersymmetry

If we assume that the swampland conjectures, etc. regarding de sitter vacuas existence in the string / F-theory landscape turn out to be incorrect (and therefore we can assume the problem is well-...
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General expression for a Scalar Superfield with ${\cal N = 1}$ in $D = 10$

I need to write explicitly the most general form of a scalar superfield in 10 dimensions up to second order in grassman variables $\theta^\alpha$. I know that up to first order one can write \begin{...
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Every theory with global SUSY is a free boson?

I'm reading this (review?) article https://www.sciencedirect.com/science/article/pii/0370157391901175 on topological field theories. In section 3.2 (page 142) they seem to be claiming that for any ...
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MSSM in 2020 and naturalness, state of art?

My question is simple. Given the current LHC and pre-LHC data bounds, can we safely say (an under what odds or conditions) that (pick one) The MSSM is unlikely to be true. The MSSM can yet be true ...
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Worldline formulation of QFT

Exist formulation of bosonic scalar field theory using action: $$ S= \frac{1}{2}\int dt\; \sqrt{g}\left(g^{tt} G_{\mu\nu} \partial_t X^\mu \partial_t X^\nu - m^2\right) $$ Also exist formulation of ...
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Why the SUSY particles of fermions have spin 0 but not 1? [duplicate]

As the supersymmetric particles have spin which differs by half, why cant the superpartners have a spin = 1. Why does it always have to be 0?
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Amplituhedron without SUSY

I was reading around about the Amplituhedron (there are many topics on this SE or in other places for discussions outside this), and I was wondering, is supersymmetry required to make it work or to ...
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How does the $D$-brane geometry influence the gauge symmetries?

I am trying to understand why the $D$-brane structure of a string theory matters for string phenomenology. From what I understood from Wikipedia, the $D$-brane structure determines the gauge ...
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$\mathcal{N}=4$ Super-Yang-Mills (SYM) and the Coulomb branch?

$\mathcal{N}=4$ Super-Yang-Mills (SYM) theory is the maximally supersymmetric gauge theory in four dimensions and is an excellent playground to investigate new techniques in amplitude and Wilson loop ...
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Can supersymmetry be extended to include anyons for 3+1D superstrings?

Are there no-go theorems and the like proving that there is no generalization of supersymmetry to fractional spins either in general or for superstrings in four dimensions? If so, are there ...
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Layman's questions about Supersymmetry

Please help me with two very silly questions. Assuming supersymmetry is correct, why don't we observe the superpartners of the Standard Model particles at ordinary energies? Why do we have to search ...
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Unitarity/Hermiticity condition for $osp(m,n|\mathbb{C})$ superalgebra

According to Dictionary on Lie Superalgebras (page 82), the compact form of $OSP(m,n|\mathbb C)$ Lie superalgebra must satisfy $M^{\text st}H\,M=1$ and $M^{\ddagger}M=1$ (is this the unitarity ...
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What is the $R$-symmetry group for ${\cal N}=6$ supergravity in $D=4$ dimensions?

What is the $R$-symmetry group for ${\cal N}=6$ supergravity in $D=4$ dimensions?
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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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Factorising the supersymmetric oscillator Hamiltonian: what (anti)commutes?

In this paper on supersymmetry, the Hamiltonian for the supersymmetric oscillator is given: $$H = \frac12 p^2 + \frac12 \omega^2 x^2 + \omega\bar\psi\psi.$$ Furthermore, its factorisation is given as $...
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Expand superspace function into component form

In 2D (1,1) superconformal field theory, the invariant "distance" between two points $Z_1=(z_1,\theta_1)$ and $Z_1=(z_1,\theta_1)$ in superspace is $$Z_{12}=z_1-z_2-\theta_1\theta_2.$$ My question ...
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Difference between sign conventions in the action of $\mathcal{N}=4$ SYM

In the paper called Wilson Loops in N=4 Supersymmetric Yang-Mills Theory, the authors define the action for the $\mathcal{N}=4$ Supersymmetric Yang-Mills (SYM) theory including the following term: $$...
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Why D-brane can be attached to NS5 branes?

What is NS5 brane? Is it possible (in analogy with D-brane) understand appearance of NS5 brane in perturbative string spectrum? Why D-brane can be attached to NS5 branes?
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How can we demand $N=2$ supersymmetry on the worldsheet?

I have been trying to understand why one should look into $c=9, N=2$ superconformal models like the Gepner models or the Kazama-suzuki models, and I am quite confused. This is what I understood from ...
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$(0,2)$ 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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