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We introduce the theoretical framework we use to study the bewildering variety of phases in condensed--matter physics. We emphasize the importance of the breaking of symmetries, and develop the idea of an order parameter through several…

Important progress in understanding the behavior of hadronic matter at high density has been achieved recently, by adapting the techniques of condensed matter theory. At asymptotic densities, the combination of asymptotic freedom and BCS…

This paper reviews the new highly interdisciplinary research field studying the behavior of condensed matter systems exposed to radiation. The paper highlights several relevant examples of recent advances in the field and provides a roadmap…

This article is meant as a gentle introduction to the "topological terms" that often play a decisive role in effective theories describing topological quantum effects in condensed matter systems. We first take up several prominent examples,…

The methods of quantum field theory are widely used in condensed matter physics. In particular, the concept of an effective action was proven useful when studying low temperature and long distance behavior of condensed matter systems. Often…

The topic of the review is the application of new ideas of unconventional quantum states to the physics of condensed matter, in particular of solid state, in the context of modern field theory. A comparison is made with classical papers on…

Ideas from quantum field theory and topology have proved remarkably fertile in suggesting new phenomena in the quantum physics of condensed matter. Here I'll supply some broad, unifying context, both conceptual and historical, for the…

In the past few years a wealth of high quality data has made possible to test current theoretical ideas about the properties of hadrons subject to extreme conditions of density and temperature. The relativistic heavy-ion program carried out…

We give a pedagogical introduction to quantum anomalies, how they are calculated using various methods, and why they are important in condensed matter theory. We discuss axial, chiral, and gravitational anomalies as well as global…

In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction…

In this chapter I discuss the impact of concepts of Quantum Field Theory in modern Condensed Physics. Although the interplay between these two areas is certainly not new, the impact and mutual cross-fertilization has certainly grown…

High energy physics features many ingenious tools for extracting finite results from formally divergent expressions. This brief note argues from a new perspective that all such formal infinities are meaningful markers of new physics. As…

Physics beyond the standard model can affect top-quark physics indirectly. We describe the effective field theory approach to describing such physics, and contrast it with the vertex-function approach that has been pursued previously. We…

We present evidence that a special class of gravitationally-coupled hidden sectors, in which conformal invariance is dynamically broken in a controlled way, exhibit the properties of dark energy. Such quantum field theories may appear while…

This paper argues that the physics of condensed matter cannot be fully reduced to the supposedly fundamental quantum mechanical theory for all the atoms of which the system consists. In fact, there are many reasons to reject the idea that…

The properties of nuclear matter are studied in the cut-off field theory. It is found that, under the Hartree approximation, the small cut-off makes the equations of state hard, especially at higher densities. The theory is modified in the…

Quantum field theories with an energy gap can be approximated at long-range by topological quantum field theories. The same should be true for suitable condensed matter systems. For those with short range entanglement (SRE) the effective…

Topology, a well-established concept in mathematics, has nowadays become essential to describe condensed matter. At its core are chiral electron states on the bulk, surfaces and edges of the condensed matter systems, in which spin and…

Topology forms a cornerstone in modern condensed matter and statistical physics, offering a new framework to classify the phases and phase transitions beyond the traditional Landau paradigm. However, it is widely believed that topological…

We review recent progress and a number of future directions for applications of effective field theory methods to condensed matter systems broadly defined. Our emphasis is on areas that have allowed a fertile exchange of ideas between high…