# 3D mirror symmetry

In theoretical physics, 3D mirror symmetry is a version of mirror symmetry in 3-dimensional gauge theories with N=4 supersymmetry, or 8 supercharges. It was first proposed by and Nathan Seiberg, in their 1996 paper "Mirror symmetry in three-dimensional gauge theories", as a relation between pairs of 3-dimensional gauge theories, such that the Coulomb branch of the moduli space of one is the Higgs branch of the moduli space of the other. It was demonstrated using D-brane cartoons by and Edward Witten 4 months later, where they found that it is a consequence of S-duality in type IIB string theory. Four months later 3D mirror symmetry was extended to N=2 gauge theories resulting from supersymmetry breaking in N=4 theories. Here it was given a physical interpretation in terms of vortices. In 3-dimensional gauge theories, vortices are particles. BPS vortices, which are those vortices that preserve some supersymmetry, have masses which are given by the FI term of the gauge theory. In particular, on the Higgs branch, where the squarks are massless and condense yielding nontrivial vacuum expectation values (VEVs), the vortices are massive. On the other hand, Intriligator and Seiberg interpret the Coulomb branch of the gauge theory, where the scalar in the vector multiplet has a VEV, as being the regime where massless vortices condense. Thus the duality between the Coulomb branch in one theory and the Higgs branch in the dual theory is the duality between squarks and vortices. In this theory, the instantons are 't Hooft–Polyakov magnetic monopoles whose actions are proportional to the VEV of the scalar in the vector multiplet. In this case, instanton calculations again reproduce the nonperturbative super potential. In particular, in the N=4 case with SU(2) gauge symmetry, the metric on the moduli space was found by Nathan Seiberg and Edward Witten using holomorphy and supersymmetric nonrenormalization theorems several days before Intriligator and Seiberg's 3-dimensional mirror symmetry paper appeared. Their results were reproduced using standard instanton techniques. (Wikipedia).

Alessandro Chiodo - Towards a global mirror symmetry (Part 1)

Mirror symmetry is a phenomenon which inspired fundamental progress in a wide range of disciplines in mathematics and physics in the last twenty years; we will review here a number of results going from the enumerative geometry of curves to homological algebra. These advances justify the i

Reflectional Symmetry

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From playlist Geometry

Reflecting a triangle over the y axis

👉 Learn how to reflect points and a figure over a line of symmetry. Sometimes the line of symmetry will be a random line or it can be represented by the x or y-axis. Either way when reflecting a point and or figure over the line of symmetry it is important to think of flipping the figure

From playlist Transformations

How to reflect a figure over a line of symmetry ex 1

👉 Learn how to reflect points and a figure over a line of symmetry. Sometimes the line of symmetry will be a random line or it can be represented by the x or y-axis. Either way when reflecting a point and or figure over the line of symmetry it is important to think of flipping the figure

From playlist Transformations

Reflecting a triangle over a line of symmetry

👉 Learn how to reflect points and a figure over a line of symmetry. Sometimes the line of symmetry will be a random line or it can be represented by the x or y-axis. Either way when reflecting a point and or figure over the line of symmetry it is important to think of flipping the figure

From playlist Transformations

Physics 11.1.3a - Spherical and Parabolic Mirrors

Spherical and Parabolic mirrors. From the Physics course by Derek Owens. The distance learning class is available at www.derekowens.com

From playlist Physics - Reflection and Refraction

Learn how to reflect a figure over a line of symmetry

👉 Learn how to reflect points and a figure over a line of symmetry. Sometimes the line of symmetry will be a random line or it can be represented by the x or y-axis. Either way when reflecting a point and or figure over the line of symmetry it is important to think of flipping the figure

From playlist Transformations

Reflecting a figure over a line of symmetry when it is on both sides

👉 Learn how to reflect points and a figure over a line of symmetry. Sometimes the line of symmetry will be a random line or it can be represented by the x or y-axis. Either way when reflecting a point and or figure over the line of symmetry it is important to think of flipping the figure

From playlist Transformations

How to reflect a line segment over the y=x line

👉 Learn how to reflect points and a figure over a line of symmetry. Sometimes the line of symmetry will be a random line or it can be represented by the x or y-axis. Either way when reflecting a point and or figure over the line of symmetry it is important to think of flipping the figure

From playlist Transformations

Geometric Langlands and 3d Mirror Symmetry (Lecture 2) by Sam Raskin

Program Quantum Fields, Geometry and Representation Theory 2021 (ONLINE) ORGANIZERS: Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pandi

Richard Rimanyi - Stable Envelopes, Bow Varieties, 3d Mirror Symmetry

There are many bridges connecting geometry with representation theory. A key notion in one of these connections, defined by Maulik-Okounkov, Okounkov, Aganagic-Okounkov, is the "stable envelope (class)". The stable envelope fits into the story of characteristic classes of singularities as

MagLab Theory Winter School 2019: Bogdan A. Bernevig "Theory"

Topic: Topological Quantum Chemistry: Theory The National MagLab held it's seventh Theory Winter School in Tallahassee, FL from January 7th - 11th, 2019.

From playlist 2019 Theory Winter School

3D Gauge Theories: Vortices and Vertex Algebras (Lecture 2) by Tudor Dimofte

PROGRAM: VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual fie

From playlist Vortex Moduli - 2023

3d N = 4 Super-Yang-Mills on a Lattice by Arthur Lipstein

Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to

Supersymmetric Ground States of 3rd N=4 Theories on a Riemann surface by Heeyeon Kim

Program Quantum Fields, Geometry and Representation Theory 2021 (ONLINE) ORGANIZERS: Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pandi

Viorica Patraucean: Mirror-symmetry in images and 3D shapes

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Mathematical Aspects of Computer Science

3D Gauge Theories: Vortices and Vertex Algebras (Lecture 2) by Tudor Dimofte

PROGRAM: VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual fie

From playlist Vortex Moduli - 2023

Geometric Langlands and 3d Mirror Symmetry (Lecture 1) by Sam Raskin

Program Quantum Fields, Geometry and Representation Theory 2021 (ONLINE) ORGANIZERS: Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pandi

Reflecting a triangle over the y=x line

👉 Learn how to reflect points and a figure over a line of symmetry. Sometimes the line of symmetry will be a random line or it can be represented by the x or y-axis. Either way when reflecting a point and or figure over the line of symmetry it is important to think of flipping the figure

From playlist Transformations