Questions tagged [supersymmetry]

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

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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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Could higher-dimensional quantum field theories be obtained as continuum limits of lattice models?

Traditional lore, based mostly on lagrangians and perturbation theory, said that nontrivial quantum field theories exist only in $d$-dimensional spacetime with $d\leq 4$. Now the lore is changing: at ...
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General and geometric prescription of Picture-changing operator (PCO), Polchinski Vol.2, section 12.5

In section 12.5, Polchinski tried to give a general description of PCO from a super-riemann surface view. He gave the generalized amplitude, The measure on supermoduli space The expression $(5.4.19)$ ...
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How Randall-Sundrum model has solved the hierarchy problem?

I'm trying to understand how the RS model solved the hierarchy problem from this mass relation $$ M^2_p = \frac{M^3}{k} \Large[1- e^{-2k\pi r} \Large],$$ Equ. 16 in their paper: https://arxiv.org/abs/...
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The hierarchy problem

I recently read a couple of scenarios to solve the hierarchy problem: the huge ratio between the electroweak scale $M_W$ of order $100-1000 $ GeV and the Planck scale $\sim 10^{19}$ GeV I think I ...
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Does planar (or non-planar) ${\cal N}=4$ SYM contain bound states?

Does planar/large number of colors ${\cal N}=4$ SYM contain bound states at strong or weak coupling? Are there bound states in the non-planar limit at strong or weak coupling?
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Why was the supersymmetry super?

The Wikipedia page stated that In a supersymmetric theory the equations for force and the equations for matter are identical. And the supersymmetry was also stated to be the correspondence between ...
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Calculating the variation of an operator in two different ways

Let $$ H_{T}=\dot{x}^{I}\frac{\partial}{\partial \psi^{I}}T(x,\psi) $$ and consider the transformation: $$ x^{I}\mapsto x^{I}+i\epsilon\psi^{I} \\ \psi^{I}\mapsto\psi^{I}-2\epsilon\dot{x}^{I} $$ where ...
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Realistic String Theories without Supersymmetry

In a podcast with Cumrun Vafa (https://www.youtube.com/watch?v=yppqz12ngbM&t=654s with the relevant part from 35:30 to 35:50), Vafa mentioned that there exists string theories that can describe ...
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Calculating amplitude for supersymmetric process in MSSM

Consider the following process $t_L+t^c_R\leftrightarrow e_r + e^c_L$ mediated by the neutral component of the higgs field: which involves the scattering between top quarks that results in a RH ...
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Why are there only two 496-dim. gauge groups $E_8\times E_8$ and $SO(32)$ allowed in string theory? Why not $E_8\times U(1)^{248}$ or $U(1)^{496}$?

While constructing anomaly-free string theories with $\mathcal N=1$ supersymmetry (16 supercharges constituting a Majorana-Weyl spinor), we learn that the gauge group must be 496-dimensional in order ...
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SUSY and van der Waerden spinor notation

I am currently trying to read into SUSY and I am running into trouble with the van der Waerden spinor notation for Weyl spinors. I am looking for resources that construct and justify the index ...
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Can I just add a cosmological constant to an on-shell supergravity action?

Suppose one has some supergravity Lagrangian $\mathcal{L}_\text{sugra}$ in flat (Minkowski) space. Moreover, assume that this Lagrangian is on-shell, in the sense that the auxiliary fields have been ...
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Have we ruled out the Minimal Supersymmetric Standard Model (MSSM)?

This question is inspired by a Physics Stackexchange question posted 8 years ago (The future of supersymmetry). The question that I have is very similar to the question in the above link, except that ...
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Meaning of "Minimal" in "Minimal Supersymmetric Standard Model"

From what I am aware of, the LHC has ruled out the Minimal Supersymmetric Standard Model (MSSM), or at least highly constrain it. "Minimal" means that supersymmetry is introduced into the ...
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Quiver Mechanics

What do you suggest as an essential and introductory set of references in Physics literature for learning quivers? Any textbook?
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Some Identities Presented in Peskin and Schroeder Problem 3.5 (Supersymmetry)

I am using the solutions for Introduction to Quantum Field Theory by Dr. Zhong-Zhi Xianyu. Right under equation $(3.41)$, the author states that $$(\sigma ^2)^T = -\sigma^2.$$ Why is this true? ...
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CFTs describing branes

In this paper section 3, the author describes how a $U(N) \;\mathcal{N}=4$ SYM theory can be coupled to 2 boundary 3D CFTs. Then the boundary CFT would describe the low-energy physics of $N$ semi-...
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Future Plans for Searches for Supersymmetry in the LHC

Due to the failure of the LHC to discover supersymmetry so far (July 2021), the simplest and the likeliest supersymmetric models (e.g. the MSSM) have been ruled out, and the confidence in ...
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Integral relation on Lie (Super)algebra

I have the following integral relation where $X$ is an element of a Lie (super)algebra, $Y_i$ are functions on the respective Lie group and $M$ is an element of the Lie group: $$Y_1(M)=\int{D}Xe^{-\...
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Status of supersymmetry in condensed matter physics (2021)

I recently came across an article in Physical Review Letters titled Realization of Supersymmetry and Its Spontaneous Breaking in Quantum Hall Edges which claims that $N=(1,0)$ SUSY could in theory be ...
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2D Wess-Zumino SUSY action invariance

I'm trying to show that the action \begin{equation} S=-\frac{1}{2}\int d^2x (\partial_\mu\phi\partial^\mu\phi+\overline{\psi}\gamma^\mu\partial_\mu\psi) \end{equation} is invariant under the SUSY ...
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$SU(2)$ gauge SUSY with Affleck-Dine-Seiberg term

Consider SUSY gauge theory with $SU(2)$ group and matter fields $Q$ and $\bar{Q}$ in fundamental and anti-fundamental representations correspondently and the following superpotential: $$W=\frac{{\...
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How can this Superconformal Field Theory anticommutator be computed for specific charges?

I'm following Kinney, Maldacena... work on the superconformal index. (https://arxiv.org/abs/hep-th/0510251, see the appendix for conventions) It is given in the appendix the anticommutator ...
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Why is life impossible in the supersymmetric Minkowski vacuum?

I read in several sources that the existence of life is impossible in the supersymmetric Minkowski vacuum (also called the terminal vacuum, the true vacuum or the global minimum). Why? After all, ...
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Supergravity 3-form $C$ fields from 2d string worldsheets

In supergravity, there are 3-form fields known as C fields. However, according to string theory, the fundamental degrees of freedoms are from string worldsheets (so at most they are fundamentally 2d). ...
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The cross on Feynman diagrams

In figure (a), in the upper part of the loop, What is the meaning of the cross between smuon and the node of selectron and photino?
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Difference between moduli spaces of supersymmetric vs non-supersymmetric theories?

I have a basic conceptual question regarding the difference between moduli spaces in supersymmetric vs non-supersymmetric theories. In usual non-supersymmetric theories, the existence of flat ...
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Conventions for graded wedge product in supergeometry

There are two conventions for the graded exterior product on superspace (see https://ncatlab.org/nlab/show/signs+in+supergeometry): $$\alpha \wedge \beta = (-1)^{pq+|\alpha||\beta|}\beta\wedge\alpha \;...
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$SU(2)$ gauge supersymmetric theory and superpotential

I am currently studying supersymmetry and I came across a superpotential of the following form $$W=\frac{\Lambda^5}{\bar{Q}Q}+m\bar{Q}Q.$$ The first term is said to appear as a result of non-...
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Motivation of Keeping Supersymmetry in String Compactification

In Candelas, Horowitz, Strominger, and Witten's famous paper [1] about string compactification, they ask that supersymmetry should not be broken in the resulting 4d theory. Then combined with other ...
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Trouble understanding the supersymmetric localization argument

A standard technique in supersymmetric quantum field theory is localization. Due to supersymmetry, one can show that only a small subset of the space of all field configurations contributes to the ...
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Calculation of an amplitude using the Grassmannian approach (amplituhedron)

In the following review paper on scattering amplitudes, by Elvang and Huang: https://arxiv.org/abs/1308.1697 they calculate the amplitude for 6 particles with half of positive helicity and half of ...
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In what meaningful way can we talk about the generators of the super-Poincaré algebra being "spinors" or "4-vectors" because of their indices?

It is often presented without much justification that the generators of the super-Poincaré algebra carry indices that imply they are elements of a representation space of the Poincaré algebra. In ...

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